Answer :
The 1st graph shows a radical expression, where:
[tex]f(x) = \sqrt{x} [/tex]
to find the inverse, replace f(x) with y, switch the x and the y, then solve for y
[tex]f(x) = \sqrt{x} ... \: y = \sqrt{x} \\ x = \sqrt{y} \\ {( \sqrt{y})}^{2} = {x}^{2} \\ y = g(x) = {x}^{2} [/tex]
The only graph showing exponential growth is the 2nd graph (note how at 1 it's 1, at 2 it's 4, at 3 it will be 9, etc.)
[tex]f(x) = \sqrt{x} [/tex]
to find the inverse, replace f(x) with y, switch the x and the y, then solve for y
[tex]f(x) = \sqrt{x} ... \: y = \sqrt{x} \\ x = \sqrt{y} \\ {( \sqrt{y})}^{2} = {x}^{2} \\ y = g(x) = {x}^{2} [/tex]
The only graph showing exponential growth is the 2nd graph (note how at 1 it's 1, at 2 it's 4, at 3 it will be 9, etc.)
Given that we have the graph of f(x), we want to see which one is the graph of its inverse. The correct option is B, the third graph.
Remember that two functions f(x) and g(x) are inverses if:
f(g(x)) = g(f(x)) = x
This also means that if:
f(x) = y
then g(y) = x.
So we basically should have the exact same graph of f(x), but we just "interchange" the two axes.
From this, we can see that the correct option is the third graph (the one where the curve goes upwards. So the correct option is B.
If you want to learn more about inverse functions, you can read:
https://brainly.com/question/10300045
