Inverses

Front

What is the inverse of g(x)?

Back

g^-1(x)

Front

Are these functions inverses? f(x) = x²-3, g(x) = 2x+8

Back

No

Front

Calculate g(f(2)) if f(x) = x²-3 and g(x) = 2x+8.

Back

10

Front

If f(x) passes through (1, 4) and (4, 6), what points does f^-1(x) pass through?

Back

(4, 1) and (6, 4)

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function.

Front

If f(x) = 3x + 2, what is f^-1(x)?

Back

f^-1(x) = (x - 2)/3

Front

What is the relationship between a function and its inverse?

Back

If f(x) takes x to y, then f^-1(y) takes y back to x.

Front

How do you find the inverse of a function algebraically?

Back

Swap x and y, then solve for y.

Front

What is the graphical representation of inverse functions?

Back

They are reflections over the line y = x.

Front

What is the condition for two functions to be inverses?

Back

f(g(x)) = x and g(f(x)) = x for all x in the domain.