Exercises : Functions and graphs

Functions and graphs

1.    Given fg(x) = x² + 1. Find

a)    g(x) if f(x)=1-2x

b)    f(x) if g(x)=x+3

ans:

a)    –x²/2

b)    X² – 6x + 10

2.    On the same axes, sketch the following exponential functions

a)    f(x) = 3^-x

b)    f(x) = 2 + 3^x

3.    On the same axes, sketch the following logarithmic functions

a)    f(x) = log ₂ (x + 2)

b)    f(x) = 3 + log ₂ x

c)    f(x) = log ₂ (-x)

5.    Given f(x) = 2^3x. Find the inverse function. Hence, sketch the graph of f(x) = 2^3x and its inverse. State the domain and range of the function f(x) = 2^3x and its inverse.