Question

What is the range of f(x)=e^3(x-2)+7?​

Answer 1

Step-by-step explanation:

We have to find the range of f(x) = e^{3(x-2)}+7e

3(x−2)

+7 .

let y = f(x) = e^{3(x-2)}+7e

3(x−2)

+7

⇒y-7 = e^{3(x-2)}e

3(x−2)

taking log base e we get,

⇒ln(y - 7) = 3(x - 2)

⇒ln(y - 7)/3 = x - 2

⇒ln(y - 7)/3 + 2 = x

⇒x = f(y) = ln(y - 7)/3 + 2

now find the domain of f(y), you will get the range of function, f(x).

for log to be defined, (y - 7) > 0

domain of f(y) , y > 7

Hope it helps u.