function composition

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. It is denoted as (f ° g)(x) = f(g(x)).

Front

If f(x) = 2x + 3 and g(x) = x^2, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(x^2) = 2(x^2) + 3 = 2x^2 + 3.

Front

What is the notation for function composition?

Back

The notation for function composition is (f ° g)(x), which means f applied to g of x.

Front

If f(x) = x + 1 and g(x) = 3x, what is (g ° f)(2)?

Back

(g ° f)(2) = g(f(2)) = g(2 + 1) = g(3) = 3(3) = 9.

Front

What is the result of f(g(x)) if f(x) = x^2 and g(x) = x + 2?

Back

f(g(x)) = f(x + 2) = (x + 2)^2 = x^2 + 4x + 4.

Front

If f(x) = x^2 and g(x) = 2x, what is (f ° g)(1)?

Back

(f ° g)(1) = f(g(1)) = f(2) = 2^2 = 4.

Front

What is the value of g(f(3)) if f(x) = x - 1 and g(x) = 3x + 2?

Back

g(f(3)) = g(3 - 1) = g(2) = 3(2) + 2 = 8.

Front

If f(x) = 3x + 1 and g(x) = x^2, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(x^2) = 3(x^2) + 1 = 3x^2 + 1.

Front

What is the output of f(g(4)) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

f(g(4)) = f(3(4) + 1) = f(13) = 13^2 + 13 = 182.

Front

If f(x) = x^2 and g(x) = x + 1, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(x + 1) = (x + 1)^2 = x^2 + 2x + 1.