function composition

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, then the composition of f and g is denoted as f(g(x)).

Front

How do you find f(2) if f(x) = x^2 - 4?

Back

f(2) = 2^2 - 4 = 0.

Front

What is the result of f[g(5)] if f(x) = x^2 + 1 and g(x) = 2x?

Back

g(5) = 2(5) = 10, then f(g(5)) = f(10) = 10^2 + 1 = 101.

Front

If f(a) = a^2 + a - 3 and g(a) = 3a, what is f(g(a))?

Back

f(g(a)) = f(3a) = (3a)^2 + (3a) - 3 = 9a^2 + 3a - 3.

Front

What is g(5) if g(x) = 15x?

Back

g(5) = 15(5) = 75.

Front

If f(g(x)) = 3x - 16, what is the composition of f and g?

Back

The composition f(g(x)) means you first apply g to x, then apply f to the result.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you evaluate f(g(x))?

Back

To evaluate f(g(x)), first calculate g(x), then substitute that result into f.

Front

What is the difference between f(x) and g(x)?

Back

f(x) and g(x) are two different functions that can have different rules or formulas.