Algebra HW Help

Question

a) Show that f(x)=4x+3 defines a one-to-one function.

(b) Write an equation for f^-1(x).

(c) Graph y=f(x) and =f^-1(x) on the same coordinate system.

Assume that f(a)=f(b). That is,

4a + 3 =

Simplifying, we get

a =

Answer 1

graph f(x), it's a linear equation, upward sloping. It passes the vertical line test for a function

the inverse function is found by switching x and y

change y = 4x + 3 to

x = 4y + 3 and solve for the new y

4y = x-3

y = (x-3)/4

f^-1 = x/4 - 3/4

if f(a) = f(b) then a=b