Excel in math and science.

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Functions

Function Misconceptions

$f$ and $g$ are two functions such that $(f \circ g)(3)=5$

What is the value of $(g \circ f)(3)$ ?

\frac{1}{5}

-\frac{1}{5}

-5 It is impossible to determine with the information given

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by Brilliant Staff

If $f$ is a function with domain $\mathbb{R}$ and range $\mathbb{R}$ , does there exist a function $g$ such that $g(x) = f^{-1}(x)$ ?

Always Not necessarily Never

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by Brilliant Staff

In the above image, the red graph is a graph of $y=f(x)$ , for some function $f$ .

What transformation of $f$ will produce the blue graph in the above graph?

y=f(x-3)

y=f(x)+3

y=f(x+3)

y=f(x)-3

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by Brilliant Staff

$f(x)$ is a function with domain $\mathbb{R}.$

$g(x)$ is a horizontal transformation of $f(x)$ such that $g(x) = f(x+k).$

$h(x)$ is a vertical transformation of $f(x)$ such that $h(x) = f(x)+k.$

If you choose $f(x)$ carefully, is it possible that $g(x)$ might equal $h(x)$ for all $x$ ?

There are no functions,

f(x),

for which it's possible. There is one unique,

f(x),

for which it's possible. There are infinitely many functions,

f(x),

for which it's possible.

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by Brilliant Staff

$f$ is a function whose domain is $\mathbb{R}$ .

$g$ is a function such that $g(x)=f^{-1}(x)$

True or false: The domain of $g$ must also be $\mathbb{R}$ .

True False

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by Brilliant Staff