Answer:
[tex]\boxed{\pink{\sf Option \ (1) \ is \ correct . }}[/tex]
Step-by-step explanation:
Given function to us is ,
[tex]\implies y = 5x^2 + 10 [/tex]
And, we need to find the inverse of the equation.
So , for that firstly replace x with y . The equation becomes
[tex]\implies x = 5y^2 + 10 [/tex]
Now , next we need to solve for y .
[tex]\implies x = 5y^2 + 10 \\\\\implies 5y^2 = x - 10 \\\\ \implies y^2 = \dfrac{x-10}{5} \\\\\implies y = \sqrt{\dfrac{x-10}{5}} [/tex]
Now , replace y for [tex]f^{-1}(x)[/tex]
[tex]\underline{\boxed{\orange{\tt \implies f^{-1}(x) = \pm\sqrt{\dfrac{x-10}{5}}}}}[/tex]
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.