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Elanso [62]
3 years ago
9

Define $g$ by $g(x)=5x-4$. If $g(x)=f^{-1}(x)-3$ and $f^{-1}(x)$ is the inverse of the function $f(x)=ax+b$, find $5a+5b$.

Mathematics
1 answer:
Slav-nsk [51]3 years ago
8 0

Answer:

<h2>2</h2>

Step-by-step explanation:

Given g(x)=5x-4 and g(x)=f^{-1}(x)-3

Substituting g(x) =  5x-4 into the second equation we have;

5x-4 =  f^{-1}(x)-3

f^{-1}(x) = 5x-4+3

f^{-1}(x) = 5x-1

To get f(x), let us first make y to be equal  f^{-1}(x)

y = 5x-1

expressing x in terms of y to get f(x), we have;

5x = y+1

x = y/5+1/5

replacing y with x, we will have;

y = x/5 + 1/5

F(x) = x/5 + 1/5

Comparing x/5 + 1/5 with ax+b, a = 1/5 and b = 1/5

5a + 5b = 5(1/5)+ 5(1/5)

5a+5b = 1+1

5a+5b = 2

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Assoli18 [71]

The value of x in x^yz = y^2 is x = \sqrt[yz]{y^2}

<h3>How to solve for x?</h3>

The equation is given as:

x^yz = y^2

Rewrite the equation properly as follows

x^{yz} = y^2

Take the yz root of both sides

\sqrt[yz]{x^{yz}} = \sqrt[yz]{y^2}

Apply the law of indices

x^{\frac{yz}{yz}} = \sqrt[yz]{y^2}

Divide yz by yz

x = \sqrt[yz]{y^2}

Hence, the value of x in x^yz = y^2 is x = \sqrt[yz]{y^2}

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7 0
2 years ago
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Pls help me It’s urgent‼️‼️
Otrada [13]

Answer:

the answer is 3/10

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7 0
3 years ago
Someone help me please !!!! Will mark Brianliest !!!!!!!!!!!!!!!! ​
alexdok [17]

Answer:

  • See below

Step-by-step explanation:

Let the amount charged is y and number of hours is x.

Then the equations are as below.

<u>Attorney A:</u>

  • y = 150x + 250

<u>Attorney B:</u>

  • y = 175x + 150

<u>If the amounts are equal, then:</u>

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3 0
2 years ago
Jivesh brought his Model B rocket on a camping trip near the top of a mountain. He wants to model how it descends down the mount
dybincka [34]

Answer:

i. 1.63 s

ii. The negative time cannot be used in this context

Step-by-step explanation:

i. Since  h = −640t² and the rocket descends 1,690 m, h = -1,690 m (since there is a drop in height).

So,  h = -640t²

t² = h/-640

t = √(- h/640)

Substituting h into the equation, we have

t = √(- h/640)

t = √[-(-1,690)/640]

t = √2.640625

t = 1.625

t ≈ 1.63 s

ii. So, the negative time cannot be used in this context because, the height drop is negative.

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3 years ago
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Answer:

Step-by-step explanation:

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