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what is the inverse function of h(x)= -3/5x 1/2? h-1(x)=-5x 5 h-1(x)=-5/3x 5/6 h-1(x)=5/3x - 5/6 h-1(x)=5x-5

User NTP
by
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2 Answers

3 votes
Hello,

Answer B

h(x)=-3/5 x+1/2 ==>x=-3/5y+1/2
==>3/5 y=-x+1/2
==>y=-3/5 x+(1/2)/(3/5)
==>y=-3/5 x+5/6

User Neil Danson
by
7.5k points
3 votes

Answer:

B.
h^(-1)(x)=(-5x)/(3)+(5)/(6)

Explanation:

We have been given a function
h(x)=-(3)/(5)x+(1)/(2). We are asked to find the inverse function of our given function.

First of all, we replace h(x) by y as:


y=-(3)/(5)x+(1)/(2)

To find inverse of our given function we will interchange x and y variables and solve for y.


x=-(3)/(5)y+(1)/(2)

Upon subtracting 1/2 from both sides of equation, we will get:


x-(1)/(2)=-(3)/(5)y+(1)/(2)-(1)/(2)


x-(1)/(2)=-(3)/(5)y

Let us have a common denominator.


(2x)/(2)-(1)/(2)=-(3)/(5)y


(2x-1)/(2)=-(3)/(5)y

Multiplying both sides by
-(5)/(3),


-(5)/(3)*(2x-1)/(2)=-(5)/(3)*-(3)/(5)y


(-10x+5)/(2*3)=y


(-10x)/(6)+(5)/(6)=y


(-5x)/(3)+(5)/(6)=y

Replacing y by
h^(-1)(x) we will get,


h^(-1)(x)=(-5x)/(3)+(5)/(6)

Therefore, the option B is the correct choice.

Therefore,

User Jmhostalet
by
7.7k points

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