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Tems11 [23]
3 years ago
13

State of the given functions are inverses

Mathematics
1 answer:
bonufazy [111]3 years ago
3 0

Answer:

1) They are not inverses

2) They are inverses

Step-by-step explanation:

We need to find the composition function between these functions to verify if these functions are inverses. If f[g(x)] and g[f(x)] are equal to x they are inverses.

<u>1)</u>

<u>Let's find f[g(x)] and simplify.</u>

f[g(x)]=\frac{1}{2}g(x)+\frac{3}{2}

f[g(x)]=\frac{1}{2}(4-\frac{3}{2}x)+\frac{3}{2}    

f[g(x)]=\frac{7}{2}-\frac{3}{4}x

As f[g(x)] is not equal to x, these functions are not inverses.

2)

<u>Let's find f[g(x)] and simplify.</u>

f[g(n)]=\frac{-16+(4n+16)}{4}

f[g(n)]=\frac{-16+4n+16}{4}

f[g(n)]=\frac{4n}{4}

f[g(n)]=n

Now, we need to find the other composition function g[f(x)]

<u>Let's find g[f(x)] and simplify.</u>

g[f(x)]=4(\frac{-16+n}{4})+16

g[f(x)]=-16+n+16

g[f(x)]=n

Therefore, as f[g(n)] = g[f(n)] = n, both functions are inverses.

I hope it helps you!  

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