# Given the functions #g(x) = (2x) (1/2)#, #f(x) = x^2 + 1 # what is f(g(x))?

To find ( f(g(x)) ), substitute ( g(x) ) into the function ( f(x) ):

[ f(g(x)) = (g(x))^2 + 1 ]

[ f(g(x)) = ((2x)^{\frac{1}{2}})^2 + 1 ]

[ f(g(x)) = (2x)^{\frac{1}{2} \times 2} + 1 ]

[ f(g(x)) = (2x) + 1 ]

So, ( f(g(x)) = 2x + 1 ).

By signing up, you agree to our Terms of Service and Privacy Policy

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the vertical, horizontal or slant asymptotes for #(x^2-4) /( x^2-2x-3)#?
- How do you find the compositions given #f(x) = |x + 1|# and #g(x) = 3x - 2 #?
- How do you find the inverse of #f(x)=x/(x+1)#?
- How do you determine if #f(x) = sec x# is an even or odd function?
- How do you find g[h(x)] and h[g(x)] given #h(x)=2x-1# #g(x)=3x+4#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7