Question

Select the correct answer from each drop-down menu.

Consider these functions:

For x ≥ 0, the value of f(g(x)) is __
For x ≥ 0, the value of g(f(x)) is __
For x ≥ 0, functions f and g __ inverse functions.


Choices:
1. x,4x,8x
2. x,4x,8x
3. are, are not

Answer 1

Answer:

x

x

are

Step-by-step explanation:

Answer 2

For x ≥ 0, the value of f(g(x)) is x,For x ≥ 0, the value of g(f(x)) will be x and functions f and g are inverse functions.Option a from all the choices is corect.

What is a function?

A connection between independent variables and the dependent variable.is defined by the function.

Functions help to represent graphs and equations. A function is represented by two variables one is dependent and another one is an independent function.

The relation between them is shown as y if dependent and x is the independent variable;

Given function;

f(x) = 16x²

g(x)=(1/4)√x

For x ≥ 0, the value of f(g(x)) is found as;

f(x) = 16x²

$\rm f(g(x)) = 16 (\frac{1}{4} \sqrt x) ^2\\\\ f(g(x)) =\frac{16}{16} x\\\\ f(g(x)) = x$

For x ≥ 0, the value of g(f(x)) is

g(x)=(1/4)√x

$\rm g(x)=\frac{1}{4}\sqrt x \\\\ g(x ) = \frac{1}{4} \times \sqrt{16 \ x^2}\\\\ g(x) = \frac{4}{4} x \\\\ g(x) = x$

For x ≥ 0, functions f and g are  inverse functions

Let,

y=F(X)

If,

y= 16x²

x=16y²

y² = x/16

y=(1/4)√x

Hence,For x ≥ 0, the value of f(g(x)),For x ≥ 0, the value of g(f(x)) will be x and x respectively.and For x ≥ 0, functions f and g are inverse functions.

Hence, option a from all the choices is corect.

To learn more about the function refer to the link https://brainly.com/question/12431044.

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