3. Functions

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$\text{ƒ}\left(x\right)=1+2x^2$

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$\text{ƒ}\left(x\right)=-x^2$

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=x²

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$\text{ƒ}\left(x\right)=1/x^2$

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$\text{ƒ}\left(x\right)=-4x+2$

The graphs of two functions ƒ and g are shown in the figures.

Find $(\text{ƒ}\circ g)\left(2\right)$.

Use the table to evaluate each expression, if possible.

$\left(f/g\right)\left(0\right)$

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

$\left(f\text{○}g\right)(-6)$

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

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

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

$(f+g)\left(2k\right)$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. ƒ(x)=1/(x+4), g(x)=-(1/x)

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

$\text{ƒ}\left(x\right)=\surd x,g\left(x\right)=\frac{1}{(x+5)}$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. ƒ(x)=√x, g(x)=3/(x+6)

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

$\text{ƒ}\left(x\right)=\surd x,g\left(x\right)=\frac{1}{(x+5)}$

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

$\text{ƒ}\left(x\right)=\surd (x+4),g\left(x\right)=-\left(\frac{2}{x}\right)$