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Mathematics

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Cloud [144]1 year ago

6 0

The value of (fg)(x)= 3x³+ x²

<h3>What is function?</h3>

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x) = -3x+1

g(x) = $x^{2}$

Now, (fg)(x)

=f(x) * g(x)

= (-3x+1) * ( $x^{2}$ )

=-3x³+ x²

Hence, (fg)(x)= 3x³+ x²

Learn more about this concept here:

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I NEED HELP WITH QUESTION PLEASE!!<br> What is the inverse of f(x)<br> (x) = (x-4)² for x ≥ 4?

goblinko [34]

Answer:

4th choice $\bold{f^{-1}(x) = \sqrt{x} + 4}$

Step-by-step explanation:

<u>Definition of the inverse of a function</u>

A function g is the inverse of a function f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing. We can write this in terms of the composition of f and g as g(f(x))=x. The domain of f becomes the range of g and the range of f becomes the domain of g

To solve for the inverse of the function $f(x) =\left(x-4\right)^2$

Let $y=\left(x-4\right)^2$

$\mathrm{Replace}\:x\:\mathrm{with}\:y$ $\text{ and replace }\:y\:\mathrm{with}\:x$

$x=\left(y-4\right)^2$

Switch sides
$\left(y-4\right)^2=x$

Take square roots on both sides
$y-4=\pm\sqrt{x}$

Add 4 on both sides to solve for y

$y = \pm\sqrt{x} + 4$

We have two solutions

$y=\sqrt{x}+4,\:y=-\sqrt{x}+4$

To determine which one of these to be chosen not that in the given choices we can eliminate the first two since x cannot be negative

The third choice can also be eliminated since
$-\sqrt{x} + 4$ is a decreasing function for $x \ge 0$

So the last answer choice is correct and the inverse of $f(x) = (x-4)^2$

is given by $f^{-1}(x) = \sqrt{x} + 4$

Answer:4th choice $\bold{f^{-1}(x) = \sqrt{x} + 4}$

Note

Domain of (x-4)² is [4, ∞) since x ≥ 4 and (x-4)² cannot be negative

Range of (x-4)² is [0, ∞)

Domain of $\sqrt{x}\:+\:4$ is [0, ∞)

Range of $\sqrt{x}\:+\:4$ is [4, ∞)

so indeed the domain of (x-4)² has become the range of $\sqrt{x}\:+\:4$ and the range of (x-4)² has become the domain of $\sqrt{x}\:+\:4$

5 0

1 year ago

A, B and C lie on a straight line.

lilavasa [31]

Answer:

y+what ever the angle inside=180 since its on a line

180-128=52

52+z+x=180since thats always the angles of a triangle added up

52+91+x=180

add

143+x=180

-143

x=37

Hope This Helps!!!

8 0

2 years ago

After completing the following frequency table, find the mode?

Mama L [17]

1000 your welcome no problem

4 0

3 years ago

A typical container of orange juice concentrate holds 12 fluids ounces (fl oz). The standard recipe is "Mix one can of concentra

dangina [55]

$The\ standard\ recipe\ is:\\\ 12\ fl\ oz\of\ orange\ juice\ concentrate\\ and\ 3\cdot 12=36\ fl\ oz\ of cold\ water\\so\ is\ 12+36=48\ fl\ oz\ of\ mix\\\\128:48=2 \frac{2}{3} \\\\Ans.\ Olivia\ need\ \ 2 \frac{2}{3}\ cans\ of\ orange\ juice\ concentrate.$

7 0

3 years ago

I need trigometry help

Alex Ar [27]

A^2=b^2+c^2-2bc Cos(A)
(270)^2=(255)^2+(442.85)^2-2(255)(442.85)Cos(A)
A=Cos^(-1)(270^2-255^2_(442.85)^2)/(-2*255*442.85)=33.5435
solve for angle A approximately is 33.54 degrees.
sinA/a=SinB/b
Sin33.54/270=SinB/255
B=Sin^(-1)(sin33.54/270*255)approximately is 31.45.
180-31.45-33.54=115.01 is Angle C.

4 0

3 years ago