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Operations with Functions

Problems

Multiplication and Composition of Functions

Inverse Functions

Problem : If f (x) = x 2 + 3x + 2 and g(x) = 5x + 3 , what is the value of:
a) 3f (1) ?
b) 3f (x) ?
c) g(x) ?
d) 2f (x) + 3g(x) ?
e) 5f (x) - 3g(x)?

a) 18.
b) 3x 2 + 9x + 2 .
c) x + 1 .
d) 2x 2 + 21x + 13 .
e) 5x 2 + 1 .

Problem : If f (x) = 3x - 2 and g(x) = , what is the value of:
a) 2f (x) + 4g(x) ?
b) 3f (x) - g(x) ?
c) fg(x) ?

a) 6x - 4 + .
b) 9x - 6 - .
c) 3 - .

Problem : If f (x) = 2x - 1 , g(x) = 3x + 4 , and h(x) = 4x , what is the value of:
a) fg(x) ?
b) fh(x) ?
c) gh(x) ?

a) 6x 2 + 5x - 4 .
b) 8x 2 - 4x .
c) 12x 2 + 16x .

Problem : If f (x) = x 2 - 2 and g(x) = 2x + 1 , what is the value of:
a) (f + g)(x) ?
b) fg(x) ?
c) f o g(x) ?
d) g o f (x) ?

a) x 2 + 2x - 1 .
b) 2x 3 + x 2 - 4x - 2 .
c) 4x 2 + 4x - 1 .
d) 2x 2 - 3 .

Problem : If f (x) = (x - 1)2 and g(x) = 4 , what is the value of:
a) (f - g)(x) ?
b) fg(x) ?
c) f o g(x) ?
d) g o f (x) ?

a) (x - 1)2 - 4 .
b) 4(x - 1)2 .
c) 9.
d) 4.

Problem : If f (x) = x 2 - 6 and g(x) = 3x + 7 , what is the value of:
a) (f + g)(x) ?
b) fg(x) ?
c) f o g(x) ?
d) g o f (x) .

a) x 2 + 3x + 1 ?
b) 3x 3 +7x 2 - 18x - 42 ?
c) 9x 2 + 42x + 43 ?
d) 3x 2 - 11 .

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