Answered

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The function h(x) = 1/x-7 can be expressed in the form f(g(x)), where g(x) = x-7), and f(x) is defined as:f(x) =

Sagot :

Answer:

f(x) = 1 /x

Explanation:

We know that

[tex]h(x)=f(g(x))=\frac{1}{x-7}[/tex]

and

[tex]g(x)=x-7[/tex]

Now, what must be the form of f(x)?

Let us guess.

If we said

[tex]f(x)=\frac{1}{x}[/tex]

then what would be f(g(x)) in this case?

To find out we simply replace x with g(x). This gives

[tex]f(g(x))=\frac{1}{g(x)}[/tex][tex]\Rightarrow f(g(x))=\frac{1}{x-7}[/tex]

which is exactly the form we are told f(g(x)) take! This means our guess was correct and

[tex]\boxed{f(x)=\frac{1}{x}\text{.}}[/tex]

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