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Elza [17]
3 years ago
6

State if the given functions are inversesNO LINKS!!!! Part 1​

Mathematics
2 answers:
sergey [27]3 years ago
5 0

Problem 1

<h3>Answer: You are correct. They are inverses</h3>

--------------------

Explanation:

One way to see if we have an inverse pair or not is to compute these two composite functions

  • f(g(x))
  • g(f(x))

If both result in x, and just that, then we have shown that they are inverses of one another.

f(x) = (2x)/3

f(x) = (2/3)x

f(g(x)) = (2/3)*g(x)

f(g(x)) = (2/3)*(3/2)x

f(g(x)) = x

The steps to show that g(f(x)) = x are very similar

g(x) = (3/2)x

g(f(x)) = (3/2)*f(x)

g(f(x)) = (3/2)*(2/3)*x

g(f(x)) = x

So this verifies that you have the correct answer.

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

Problem 2

<h3>Answer: These functions are inverses of each other.</h3>

--------------------

Explanation:

We'll use the same idea as problem 1

f(x) = 2 - (3/4)*x

f(g(x)) = 2 - (3/4)*( g(x) )

f(g(x)) = 2 - (3/4)*( (-4/3)x + 8/3 )

f(g(x)) = 2 - (3/4)*(-4/3)x  - (3/4)*(8/3)

f(g(x)) = 2 + x - 2

f(g(x)) = x

So far so good, but we need to check the other way around as well

g(x) = (-4/3)x + 8/3

g(f(x)) = (-4/3)*( f(x) ) + 8/3

g(f(x)) = (-4/3)*( 2 - (3/4)*x ) + 8/3

g(f(x)) = (-4/3)*(2) + (-4/3)*(-3/4)*x + 8/3

g(f(x)) = -8/3 + x + 8/3

g(f(x)) = x

This verifies that f(x) and g(x) are inverses of each other.

Problems 3 and 4 will have similar steps.

Dafna11 [192]3 years ago
3 0

Step-by-step explanation:

3:

h(x)=(-3x-15)/5

let y=(-3x-15)/5

interchanging role of x &y

x=(-3y-15)/5

5x+15=-3y

y=-(5x+15)/3

h-1(x)=-(5x+15)/3

not

equal to f(x)=(-3x-6)/4

<u>G</u><u>i</u><u>v</u><u>e</u><u>n</u><u> </u><u>func</u>tion <u>are</u><u> </u><u>not</u><u> </u><u>function</u><u> </u><u>of</u><u> </u><u>each </u><u>other</u><u> </u><u>.</u>

4:

g(x)=2/3x-2/3

let

y=2/3(x-1)

interchanging role of x &y

x=2/3(y-1)

3/2x+1=y

g-1(x)=3/2x+1

not equal to f(x)=½x+1

<u>Given function are not function of each other .</u>

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