Question

What is the inverse of f(x)=√1/4x-8 -7 for x ≥ 32. (The √1/4x-8 is under the exponent the -7 is not)

A. f^-1(x)=4[(x+7)^2+8]; x ≥ -7
B. f^-1(x)=4 [(x+8)^2 +7] ; x ≥ -8
C. f^-1(x)=4 [(x+8)^2+7] ; x ≥ -8
D. f^1(x) =1/4[(x+7^2)+8] ; x ≥ -7

Please ASAP!!!!! Thanksssssss

Answer 1

The inverse of the function f(x) = √(1/4x - 8) - 7 for x ≥ 32 is f^-1(x) = 4[(x + 7)^2 + 8]. The correct option is A, where x is restricted to x ≥ -7.

To find the inverse of the function f(x) = √(1/4x - 8) - 7 for x ≥ 32, we interchange f(x) and x and solve for the new variable, denoted as f^-1(x):

Start with the original function: f(x) = √(1/4x - 8) - 7.

Replace f(x) with y: y = √(1/4x - 8) - 7.

Swap x and y: x = √(1/4y - 8) - 7.

Isolate the radical term and solve for y:

x + 7 = √(1/4y - 8),

(1/4y - 8) = (x + 7)^2,

1/4y = (x + 7)^2 + 8,

y = 4[(x + 7)^2 + 8].

Therefore, the inverse function is f^-1(x) = 4[(x + 7)^2 + 8]. However, considering the domain restrictions (x ≥ 32), the correct answer is:

A. f^-1(x) = 4[(x + 7)^2 + 8]; x ≥ -7.