If we know that f (x) is a linear function and satisfies 3f (x + 1) - 2F (x-1) = 2x + 17, then f (x) =? Each step should be described in detail,
Let f (x) = KX + B, then
f(x+1)=k(x+1)+b=kx+k+b
3f(x+1)=3kx+3k+3b
f(x-1)=k(x-1)+b=kx-k+b
2f(x-1)=2kx-2k+2b
3f(x+1)-2f(x-1)=(3kx+3k+3b)-(2kx-2k+2b)
=3kx+3k+3b-2kx+2k-2b
=kx+5k+b
∵3f(x+1)-2f(x-1)=2x+17
∴kx+5k+b=2x+17
∴k=2
5k+b=17
∴k=2,b=7
∴f(x)=2x+7
RELATED INFORMATIONS
- 1. If we know that f (x) is a function of degree and satisfies 3f (x + 1) = 2x + 17, then f (x) = () A. 23x+5B. 23x+1C. 2x-3D. 2x+5
- 2. If the function f (x) = a + 2 / 2 ^ X-1 is odd in its domain, then the value of real number a is zero
- 3. If the function f (x) = a + 2 / (2 ^ x-1) is an odd function in its domain, then the value of the real number a
- 4. It is known that the function f (x) defined on the real number set R satisfies the following conditions: (1) f (- x) = f (x) (2) f (2 + x) = f (2-x) (3) when x ∈ [0,2], the analytic formula y = 2x-1, and the analytic formula on X ∈ [- 4,0] is obtained
- 5. Given that the function y = f (x) defined on the real number set R is symmetric with respect to the straight line x = 2, and the analytic expression of X ∈ [0,2] is y = 2x-1, then the analytic expression of F (x) on X ∈ [2,4] is y = 2x-1____ .
- 6. Let f (x) be a function on R and satisfy f (0) = 1, and for any real number, f (X-Y) = f (x) - Y (2x-y + 1), the analytic expression of F (x) is obtained I don't understand the two equations. I hope I can be more detailed
- 7. It is known that f (x) is an increasing function defined on R +, and f (x / y) = f (x) - f (y) holds for any x, y ∈ R + (1) Find the value of F (1) (2) If f (4) = 1, solve the inequality f (x + 6) - f (1 / x) < 2
- 8. The increasing function f (x) defined on R + satisfies that f (x / y) = f (x) - f (y) holds for any x, y ∈ R + 1. Find f (1) (solved) the answer is 0 2. F (4) = 1, solving inequality: F (x + 6) - f (1 / x)
- 9. The function f (x) defined on R satisfies the following conditions: F (x) + F (- x) = 2 pairs of non-zero real numbers x, all of which have 2F (x) + F (1 / x) = 2x + 1 / x + 3. (1) find the analytic expression of F (x) The function f (x) defined on R satisfies the following conditions: F (x) + F (- x) = 2 pairs of non-zero real numbers x, all of which have 2F (x) + F (1 / x) = 2x + 1 / x + 3. (1) find the analytic expression of F (x) (2) Let f ^ 2 (x) - 2x under the function g (x) = root sign, y = 2 ^ (1 / 2) N-X and y = G ^ - 1 (x) respectively The function f (x) defined on R satisfies the following conditions: F (x) + F (- x) = 2 pairs of non-zero real numbers x, all of which have 2F (x) + F (1 / x) = 2x + 1 / x + 3. (1) find the analytic expression of F (x) (2) Let f ^ 2 (x) - 2x under the function g (x) = root sign, y = 2 ^ (1 / 2) N-X and y = G ^ - 1 (x) respectively Let an be the length of anbn and Sn be the sum of the first n terms of the sequence {an}. When n is greater than or equal to 2, the square of Sn is greater than 2 (S2 / 2 + S3 / 3 +...) +Sn/n)
- 10. Let f (x) be a function defined on the real number set R and satisfy the following conditions: F (x + 2) = f (x + 1) - f (x). If f (1) = Lg3 / 2, f (2) = LG15, find f (2004) Please! I'm very polite!
- 11. If we know that f (x) is a linear function and satisfies 3f (x + 1) - 2F (x-1) = 2x + 17, we can find f (x) =?
- 12. Finding f (x) by knowing that the function is a linear function and satisfies the relation 3f (x + 1) - 2F (x-1) = 2x-17
- 13. It is known that the function f (x) is a first-order function and satisfies the formula 3f (x + 1) - 2F (x-1) = 2x + 17 to find the expression of F (x)
- 14. Given that the function FX satisfies 3f (x) - 2F (1-x) = 2x + 3, find the analytic formula
- 15. It is known that f (x) is a first-order function, which satisfies 3f (x + 1) - 2F (x-1) = 2x = 17
- 16. Given that the function f (x) satisfies the condition, 2f (- x) + FX = 2x-3 (x belongs to R), find the analytic expression of F (x)
- 17. Given that the function FX satisfies 2F (x) - f (- x) = - x Λ 2 + 4x, then the expression of FX is?
- 18. Given that the function F X satisfies FX + 2F (- x) = x3-2, the analytic expression of function F X is obtained More than 50 rewards in 10 minutes
- 19. If f (x) satisfies 2F (x) - f (- x) = LG (x + 1), X belongs to the problem of (- 1.1) finding f (x)... Finding the analytic formula of function
- 20. The problem is known 2F (x) + F (1 / x) = 2x, find the analytic expression of F (x)