MATH SOLVE

4 months ago

Q:
# The graph of f(x) is shown below.(First image below)If g(x) and f(x) are inverse functions, which graph represents g(x)?A. 2nd Graph belowB. 3rd Graph belowC. 4th Graph belowD. 5th Graph below

Accepted Solution

A:

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.)