Mathematics | VITEEE 2019 | Discussion Page

Let f: R→ R, g : R→ R be two functions such that f(x) = 2x - 3, g(x) = x³ + 5. The function (fog)^-1(x) is equal to

$\left(\frac{x+7}{2}\right)^{1/3}$

$\left(x-\frac{7}{2}\right)^{1/3}$

$\left(\frac{x-2}{7}\right)^{1/3}$

$\left(\frac{x-7}{2}\right)^{1/3}$

Option D

We have, f(x) = 2x-3, g(x) = x³ + 5

(fog)x =f (x³ + 5) = 2(x³ + 5) -3 = 2x³+7

Let y= (fog)x = 2x³ + 7

$x = \left(\frac{y-7}{2}\right)^{1/3}$

(fog)^-1 $x = \left(\frac{x-7}{2}\right)^{1/3}$

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