3. Functions

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\frac{2}{x},g\left(x\right)=x+1$

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\surd (x+2),g\left(x\right)=-\left(\frac{1}{x}\right)$

Use the graphs of f and g to solve Exercises 83–90.

Find (f+g)(−3).

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\surd (x+2),g\left(x\right)=-\left(\frac{1}{x}\right)$

Use the graphs of f and g to solve Exercises 83–90.

Find (g-f) (-2).

Given functions f and g, (g∘ƒ)(x) and its domain. ƒ(x)=1/(x-2), g(x)=1/x

Use the graphs of f and g to solve Exercises 83–90.

Find the domain of ƒ + g.

Given functions f and g, find (ƒ∘g)(x) and its domain. ƒ(x)=1/(x-2), g(x)=1/x

Use the graphs of f and g to solve Exercises 83–90.

Find the domain of ƒ/g.

Use the graphs of f and g to evaluate each composite function.

(go f) (0)

Find all values of x satisfying the given conditions. f(x) = 2x − 5, g(x) = x² − 3x + 8, and (ƒ o g) (x) = 7.

Let $\text{ƒ}\left(x\right)=3x^2-4$ and $g\left(x\right)=x^2-3x-4$. Find each of the following.

$\left(f/g\right)(-1)$

Let $\text{ƒ}\left(x\right)=\text{√}(x-2)$ and $g\left(x\right)=x^2$. Find each of the following, if possible.

$\left(g\text{○ƒ}\right)\left(x\right)$

Let $\text{ƒ}\left(x\right)=\text{√}(x-2)$ and $g\left(x\right)=x^2$. Find each of the following, if possible

$\left(g\text{○ƒ}\right)\left(3\right)$