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Sergeeva-Olga [200]

3 years ago

13

. Find the inverse of the function below on the given interval and write it in the form yequalsf Superscript negative 1 Baseline

(x ). b. Verify the relationships f (f Superscript negative 1 Baseline (x ))equalsx and f Superscript negative 1 Baseline (f (x ))equalsx.

1 answer:

Elena L [17]3 years ago

8 0

Answer:

The inverse of the function is $f^{-1}(x)=\frac{x-5}{3}$ .

Step-by-step explanation:

The function provided is:

$f (x)=3x+5$

Let $f(x)=y$ .

Then the value of <em>x</em> is:

$y=3x+5\\\\3x=y-5\\\\x=\frac{y-5}{3}$

For the inverse of the function, $x\rightarrow y$ .

⇒ $f^{-1}(x)=\frac{x-5}{3}$

Compute the value of $f[f^{-1}(x)]$ as follows:

$f[f^{-1}(x)]=f[\frac{x-5}{3}]$

$=3[\frac{x-5}{3}]+5\\\\=x-5+5\\\\=x$

Hence proved that $f[f^{-1}(x)]=x$ .

Compute the value of $f^{-1}[f(x)]$ as follows:

$f^{-1}[f(x)]=f^{-1}[3x+5]$

$=\frac{(3x+5)-5}{3}\\\\=\frac{3x+5-5}{3}\\\\=x$

Hence proved that $f^{-1}[f(x)]=x$ .

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Answer:

Step-by-step explanation:

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as from attached image , we can see that its look like two right angle triangle

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3 years ago

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We have

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and

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