Function Compositions

Adding/subtracting functions

100

f(x) = x+1

g(x) = x+2

Find (f+g)(x)

(f+g)(x) = 2x+3

200

f(x) = x³+4

g(x) = x - 5

Find (f-g)(x)

(f-g)(x) = x³-x+9

300

f(x) = sqrt(x²+1)

g(x) = x^4-5

Find (f+g)(x)

(f+g)(x) = sqrt(x²+1) + x⁴ - 5

400

f(x) = 1/x

g(x) = 1/x

Find (f-g)(x)

(f-g)(x) = 0

500

f(x) = 8x+3

g(x) = (x+2)²

Find (f-g)(x)

(f-g)(x) = -x²+4x-1

Multiplying/dividing functions

100

f(x) = x²

g(x) = x³

Find (f*g)(x)

(f*g)(x) = x⁵

200

f(x) = x⁵

g(x) = x³

Find (f/g)(x)

(f/g)(x) = x²

300

f(x) = x²-4

g(x) = x²+2x-8

Find (f/g)(x)

(f/g)(x) = (x+2)/(x+4)

400

f(x) = x⁴+8

g(x) = x²+3

Find (f*g)(x)

(f*g)(x) = x⁶+3x⁴+8x²+24

500

f(x) = x²-6x+9

g(x) = x²+5x-24

Find (f/g)(x)

(f/g)(x) = (x-3)/(x+8)

Plugging into combined functions

100

If (f/g)(x) = (x-3)/(x+8), find (f/g)(4).

(f/g)(4)=1/12

200

If (f+g)(x) = 5x⁴+3x²+4x+19, find (f+g)(2).

(f+g)(2) = 119

300

f(x) = x²-3

g(x) = x²+9

Find (f*g)(5).

(f*g)(5)= 748

400

f(x) = x⁴

g(x) = x³

Find (f/g)(4,153)

(f/g)(4,153) = 4153

500

f(x) = x+4

g(x) = 4x+7

Find f(g(3))

f(g(3)) = 23

Composition of functions

100

f(x) = x+1

g(x) = x+4

Find f(g(x))

f(g(x)) = x+5

200

f(x) = x²-7

g(x) = x²+2

Find g(f(x))

g(f(x)) = x⁴-14x²+51

300

f(x) = sqrt(x+4)

g(x) = x²+12

Find f(g(x))

f(g(x)) = sqrt(x²+16)

400

f(x) = x³+2

g(x) = 2/x

Find g(f(x))

g(f(x)) = 2/(x³+2)

500

f(x) = 1/4x²

g(x) = x²-7

Find f(g(4))

f(g(4)) = 1/324

Function Inverses

100

f(x) = x-13

Find f^-1(x)

f^-1(x) = x+13

200

f(x) = 1/3x+3

Find f^-1(x)

f^-1(x) = 3x-9

300

f(x) = 10x⁷

Find f^-1(x)

f^-1(x) = (x/10)^1/7

400

f(x) = (x-2)^1/5/9

Find f^-1(x)

f^-1(x) = (9x)⁵+2

500

f(x) = 7(x^1/7+4)-9

Find f^-1(x)

f^-1(x) = (((x+9)/7)-4)⁷