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Functions $f$ and $g$ are defined on suitable domains by $f(x) = 5x$ and $g(x) = 2 ext{cos} \, x$ - Scottish Highers Maths - Question 1 - 2017

Question 1

$Functions-$f$-and-$g$-are-defined-on-suitable-domains-by-$f(x)-=-5x$-and-$g(x)-=-2-ext{cos}-\,-x$-Scottish Highers Maths-Question 1-2017.png$

Functions $f$ and $g$ are defined on suitable domains by $f(x) = 5x$ and $g(x) = 2 ext{cos} \, x$. (a) Evaluate $f(g(0))$. (b) Find an expression for $g(f(x))$.

Worked Solution & Example Answer:Functions $f$ and $g$ are defined on suitable domains by $f(x) = 5x$ and $g(x) = 2 ext{cos} \, x$ - Scottish Highers Maths - Question 1 - 2017

Step 1

Evaluate $f(g(0))$

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Answer

To evaluate $f(g(0))$ , we first need to find $g(0)$ .

Given:

g(x) = 2 ext{cos} , x,

we substitute 0 into the function:

$g(0) = 2 ext{cos}(0) = 2(1) = 2.$

Now that we have $g(0) = 2$ , we can substitute this value into the function $f$ :

$f(g(0)) = f(2) = 5(2) = 10.$

Therefore, the answer is:

$$f(g(0)) = 10.$

Step 2

Find an expression for $g(f(x))$

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Answer

To find the expression for $g(f(x))$ , we start with the function definitions:

$f(x) = 5x$ and $g(x) = 2 ext{cos} \, x.$

Now we need to substitute $f(x)$ into $g(x)$ :

$g(f(x)) = g(5x) = 2 ext{cos}(5x).$

Thus, the expression for $g(f(x))$ is:

$g(f(x)) = 2 ext{cos}(5x).$

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