Question

What is the answer to this question?

Answer 1

Answer:

$\boxed{\pink{\sf Option \ (1) \ is \ correct . }}$

Step-by-step explanation:

Given function to us is ,

$\implies y = 5x^2 + 10$

And, we need to find the inverse of the equation.

So , for that firstly replace x with y . The equation becomes

$\implies x = 5y^2 + 10$

Now , next we need to solve for y .

$\implies x = 5y^2 + 10 \\\\\implies 5y^2 = x - 10 \\\\ \implies y^2 = \dfrac{x-10}{5} \\\\\implies y = \sqrt{\dfrac{x-10}{5}}$

Now , replace y for $f^{-1}(x)$

$\underline{\boxed{\orange{\tt \implies f^{-1}(x) = \pm\sqrt{\dfrac{x-10}{5}}}}}$

As per the options provided in Question we can that option (1) mathces with our answer when we just interchanged the variables.

Hence option (1) is correct.