Advanced Functions

5.5 Solving Radical Equations

100

Solve This Equation x+2 = √5x+16

x= 4 or x=-3

200

Solve This Equation 2√x+1 = 4

x = 3

300

Solve This Equation ³√2x - 9 = 2

x = 18

400

Solve ³√x - 10 = - 7

x = 27

500

Solve 2(x + 11)^1/2 = x + 3

x = 5

5.6 Performing Function Operations

100

Let f(x) = 4(2^x) and g(x) = -3(2^x). Find (f = g)(x).

= 16 , but using a graphical approach you will get    (f +g)(4) = 16 as well. 

200

Let f(x)= 2x - 3 and g(x) = x⁴-2x³+ x Find (f+g)(x) and ( f - g)(x). 

( f +g)

300

f(x)= 2(3^x), g(x)= -6(3^x); 

= -108

400

Let f(x) = 2x - 3 and g(x) = x⁴-2x³+x. Find (f + g)(x) and (f - g)(x) and state the domain. Then evaluate (-2)

(f+g) (x)= 1x⁴-2x³+3x-3

(f - g)(x)= -x⁴+2x³+x-3

Domain for both: All real numbers

Evaluate:

(f +g)(-2)= 23                                                   

(f -g)(-2)= -37

500

Let f(x)= 2^x and g(x)=3x. Find (fg)(x) (f/g)(x).

(fg)(x)=(2²)(3x)

(f/g)(x)= 2^x/3x

5.8 Inverse of a Function

100

The inverse is f(x) =6x

The inverse is g(x)= 1/6x

200

Find the inverse of f(x)= -2x + 5

The inverse is g(x)= x - 5/ -2 

300

Find the inverse of f(x)= -1/2x + 4

The inverse is g(x) = -2(x - 4)

400

Find the inverse of f(x)= 2/3x - 1/3. 

The inverse is g(x)= 3/2x + 1/2.

500

Determine if f(x)=x³-1 is invertible

It is invertible and f^-1(x)= ³√x+1

5.7 Composition of Functions

100

Find (a) f(g(x)), (b) g(f(x)), c f(f(f)). State the Domain and range of each composition.

f(x)= 3x², g(x)= -x-2

a. Find f(g(x))                                                         b. Find g(f(x))                                                      c. Find f(f(x))

a. 3x²+12x+12

b. -3x²-2

c. The domain of f(f(x)) is all real numbers and the range is ( 0,∞ )

200

Find (a) f(g(x)), (b) g(f(x)), c f(f(f)). State the 0Domain and range of each composition.

f(x)=6x + 5, g(x)= √x+4

a. Find f(g(x))                                                           b. Find g(f(x))                                                         c. Find f(f(x))

a. 6(√x +4) +5                                                       b. √6x + 9                                                             c. The domain and range is all real numbers

300

Find (a) f(g(x)), (b) g(f(x)), c f(f(f)). State the 0Domain and range of each composition.

f(x)=-7x +1, g(x) = ³√x-2

a. Find f(g(x))                                                           b. Find g(f(x))                                                         c. Find f(f(x))

a. 07 (³√x - 2) + 1

b. ³√(-7 - 1)

c. The domain and range is all real numbers.

400

Find (a) f(g(x)), (b) g(f(x)), c f(f(f)). State the 0Domain and range of each composition.

f(x)= x - 9, g(x)=x^{3-4x +} 3

a. Find f(g(x))                                                           b. Find g(f(x))                                                         c. Find f(f(x))

a. x^3-4x-6                                                                b. (x - 9)^39-4x+3                                                      c. The domain and range are all real numbers

500

Find (a) f(g(x)), (b) g(f(x)), c f(f(f)). State the 0Domain and range of each composition.

Let f(x)= 4x - 3, g(x)= x² + 8

a. Find f(g(x))                                                           b. Find g(f(x))                                                         c. Find f(f(x))

a. 4x²+29                                                                b. 16x²-24x+17                                                      c. The domain and range are all real numbers.