Define $g$ by $g(x)=5x-4$. If $g(x)=f^{-1}(x)-3$ and $f^{-1}(x)$ is the inverse of the function $f(x)=ax+b$, find $5a+5b$.

Step-by-step explanation:

Given g(x)=5x-4 and g(x)=f^{-1}(x)-3

Substituting g(x) =  5x-4 into the second equation we have;

5x-4 =  f^{-1}(x)-3

f^{-1}(x) = 5x-4+3

f^{-1}(x) = 5x-1

To get f(x), let us first make y to be equal  f^{-1}(x)

y = 5x-1

expressing x in terms of y to get f(x), we have;

5x = y+1

x = y/5+1/5

replacing y with x, we will have;

y = x/5 + 1/5

F(x) = x/5 + 1/5

Comparing x/5 + 1/5 with ax+b, a = 1/5 and b = 1/5

5a + 5b = 5(1/5)+ 5(1/5)

5a+5b = 1+1

5a+5b = 2

it will be a cylinder. with a diameter of 8 and 4 single pieces high

step-by-step explanation:

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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