# How do you find the compositions given #f(x)=2-x# and #g(x)=2/(5-x)#?

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

To find the compositions of ( f(x) = 2 - x ) and ( g(x) = \frac{2}{5 - x} ), we substitute one function into the other.

First, we find ( f(g(x)) ): [ f(g(x)) = f\left(\frac{2}{5 - x}\right) ] [ = 2 - \frac{2}{5 - x} ] [ = \frac{10 - 2}{5 - x} - \frac{2}{5 - x} ] [ = \frac{8}{5 - x} ]

Next, we find ( g(f(x)) ): [ g(f(x)) = g(2 - x) ] [ = \frac{2}{5 - (2 - x)} ] [ = \frac{2}{3 + x} ]

So, ( f(g(x)) = \frac{8}{5 - x} ) and ( g(f(x)) = \frac{2}{3 + x} ).

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 #f^-1(x)# given #f(x)=1/x#?
- How do you find the compositions given #f(x)+3x-5# and #g(x)= sqrt(x-2)#?
- How do you find the end behavior of #F(x) = 2x^(3) + 3x^(2) - 8x -12#?
- What is the end behavior and turning points of #y = x^3 + 4x #?
- How do you find vertical, horizontal and oblique asymptotes for #(2x^3+4x-8)/(x^3-6x)#?

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