Find the inverse of f x -4- x -731-5A- 7-4-x51-3B- 4-x-731-5C- 4-x-42D- none of these

The correct option is A Option (a) Let y=f(x)=(4 (x 7)^3)^1/5 y^5=(4 (x 7)^3) (x 7)^3 =4 y^5 x=7+(4 y^5)^1/3 Replace y by x to get the answer. 7+(4 x^5)^1 ...

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Quantitative Aptitude

Functions

Find the inve...

Question

Find the inverse of $f (x) = {(4 - (x - 7)^{3})}^{\frac{1}{5}}$

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none of these

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Solution

The correct option is A
Option (a)

Let $y = f (x) = {(4 - (x - 7)^{3})}^{\frac{1}{5}}$

$y^{5} = (4 - (x - 7)^{3})$
$(x - 7)^{3} = 4 - y^{5}$
$x = 7 + (4 - y^{5})^{\frac{1}{3}}$

Replace y by x to get the answer.

$7 + (4 - x^{5})^{\frac{1}{3}}$

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Find the inverse of f(x)=(4−(x−7)3)15

The correct option is A Option (a) Let y=f(x)=(4−(x−7)3)15 y5=(4−(x−7)3) (x−7)3=4−y5 x=7+(4−y5)13 Replace y by x to get the answer. 7+(4−x5)13

Find the inverse of $f (x) = {(4 - (x - 7)^{3})}^{\frac{1}{5}}$

The correct option is A
Option (a)

Let $y = f (x) = {(4 - (x - 7)^{3})}^{\frac{1}{5}}$

$y^{5} = (4 - (x - 7)^{3})$
$(x - 7)^{3} = 4 - y^{5}$
$x = 7 + (4 - y^{5})^{\frac{1}{3}}$

Replace y by x to get the answer.

$7 + (4 - x^{5})^{\frac{1}{3}}$