Find the inverse of the following function. f(x) =^3squareroot x + 12
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2 answers:
Answer:
C. F^-1(x)=x^3-12
Step-by-step explanation:
![\sqrt[3]{x+12} =y\\\\then\\\\x+12=y^{3} \\\\then\\\\x=y^{3} -12\\\\then\\\\f^{-1}(x) =x^{3} -12](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%2B12%7D%20%3Dy%5C%5C%5C%5Cthen%5C%5C%5C%5Cx%2B12%3Dy%5E%7B3%7D%20%5C%5C%5C%5Cthen%5C%5C%5C%5Cx%3Dy%5E%7B3%7D%20-12%5C%5C%5C%5Cthen%5C%5C%5C%5Cf%5E%7B-1%7D%28x%29%20%3Dx%5E%7B3%7D%20%20-12)
Answer:
(x - 12)²/9
Step-by-step explanation:
y = 3sqr(x) + 12
Make x the subject:
y - 12 = 3sqrt(x)
(y - 12)/3 = sqrt(x)
Square both sides
(y - 12)²/9 = x
Interswitch variables
inverse function is:
(x - 12)²/9
If f(x) = (x + 12)^⅓
Then,
y = (x + 12)⅓
y³ = x + 12
y³ - 12 = x
f inverse:
x³ - 12
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