Answer:
[tex]f^{-1}(x)=\sqrt{\frac{1}{8}(-x+4)}[/tex]
Step-by-step explanation:
Given function is,
f(x) = -8x² + 4
Step to find the inverse of the function,
Step 1
Write the function in the form of an equation,
y = -8x² + 4
Step 2
Interchange the variables 'x' and 'y',
x = -8y² + 4
Step 3
Solve the equation for y,
x = -8y² + 4
x - 4 = -8y²
-x + 4 = 8y²
y² = [tex]\frac{1}{8}(-x+4)[/tex]
[tex]y=\sqrt{\frac{1}{8}(-x+4)}[/tex]
Therefore, inverse of the function f(x) will be,
[tex]f^{-1}(x)=\sqrt{\frac{1}{8}(-x+4)}[/tex]
