3. Functions

For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2.

ƒ(x)=2x^2-3x, g(x)=x^2-x+3

For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2.

ƒ(x)=3x+4, g(x)=2x-6

For the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2.

ƒ(x)=3x+4, g(x)=2x-5

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1.

(ƒ/g)(5)

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

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

Given functions f and g, find (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}x,g\left(x\right)=x+3$

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}x,g\left(x\right)=x+3$

Given functions f and g, find (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=8x+12,g\left(x\right)=3x-1$

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=-6x+9,g\left(x\right)=5x+7$

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5.

$(g\circ g)(-2)$

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5.

$(\text{ƒ}\circ g)\left(4\right)$

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.

$\text{ƒ}\left(x\right)=x^2-4x+2$

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.

$\text{ƒ}\left(x\right)=1+2x^2$

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.

$\text{ƒ}\left(x\right)=-x^2$