Combining Functions

[JSmith]

Given f(x) = x² and g(x) = x + 2, determine in standard form:
a) f(g(x))
b) g(f(x))
c) when f(g(x)) = g(f(x))

how do I go about c)?

 

[srmichael]

Given f(x) = x² and g(x) = x + 2, determine in standard form:
a) f(g(x))
b) g(f(x))
c) when f(g(x)) = g(f(x))

how do I go about c)?

Set them equal to each other and solve.

(x+2)² = x² + 2

x² + 4x + 4 = x² + 2.

Can you take it from here and solve for x?

 

[JSmith]

How does that look?

 

[srmichael]

How does that look?

You got it!