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Shalnov [3]
2 years ago
9

What is the inverse of the function f(x) = 2x + 1?

Mathematics
1 answer:
Liula [17]2 years ago
4 0

<em><u>Inverse</u></em><em><u> </u></em><em><u>Of</u></em><em><u> </u></em><em><u>Functions</u></em>

I use a certain way to find the inverse of a function.

Replace H(x) with y.

y=2x+1

Replace y and x.

x=2y+1

Find y.

x-1=2y

Divide both sides by two.

x-1/2=y

<em>The</em><em> </em><em>Answer</em><em> </em><em>Is</em>

<em>h^{ - 1} (x) =  \frac{x - 1}{2}</em>

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Answer: Choice C

h(x) = -x^4 + 2x^3 + 3x^2 + 4x + 5

===========================================

Explanation:

When reflecting the function f(x) over the y axis, we replace every x with -x and simplify like so

f(x) = -x^4 - 2x^3 + 3x^2 - 4x + 5

f(-x) = -(-x)^4 - 2(-x)^3 + 3(-x)^2 - 4(-x) + 5

f(-x) = -x^4 + 2x^3 + 3x^2 + 4x + 5

h(x) = -x^4 + 2x^3 + 3x^2 + 4x + 5

Note the sign changes that occur for the terms that have odd exponents (the terms -2x^3 and -4x become +2x^3 and +4x); while the even exponent terms keep the same sign.

The reason why we replace every x with -x is because of the examples mentioned below

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Examples:

The point (1,2) moves to (-1,2) after a y axis reflection

Similarly, (-5,7) moves to (5,7) after a y axis reflection.

As you can see, the y coordinate stays the same but the x coordinate flips in sign from negative to positive or vice versa. This is the direct reason for the replacement of every x with -x.

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Hence the values of x that make (x+3)(x+12) = 0 are x = 3 and x = 12.

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