Question

Consider the function y=4e^3x-2 . (a) What is its domain? What is the range? (b) Find the intercepts on the two axes if they exist. (c) Sketch the graph of the function showing the intercepts on the two axes, if any. (d) What is the inverse function?

Answer 1

Range: All Real Numbers

Domain: (-2, ∞)

The intercept of the graph is: (-0.231, 0) and (0, 2).

Inverse Function =
`(1)/(3)\log{(y+2)/(4)}`

Explanation:

The range is the all possible value of a function (or x) that give defined values.

The domain is the all defined values that we get from a function (or y).

There are two intercepts: x-intercept and y-intercept.

The point where the graph meets at the x-axis is known as x-intercept and the point where the graph meets at y-axis is known as the y-intercept.

Here, x-intercept is: (-0.231, 0) and y-intercept is: (0, 2).

The inverse function is inverse of that function. If the input is x and we get result y then in inverse function input is y and result is x.

Here We have,
`y=4exp(3x)-2`

⇒
`y+2=4exp(3x)`

⇒
`(y+2)/(4)=exp(3x)`

⇒
`\log(y+2)/(4)=3x`

⇒
`(1)/(3)\log{(y+2)/(4)}`