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3 years ago

Find an equation for the inverse for each of the following.

Mathematics

1 answer:

IgorLugansk [536]3 years ago

4 0

Answer:

To solve these first swap x and y, solve for y and name it inverse function

3. y = -8x + 2

x = -8y + 2
8y = -x + 2
y = -x/8 + 2/8
y = -(18)x + 1/4

f⁻¹(x) = -(18)x + 1/4

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

4. y = (2/3)x - 5

x = (2/3)y - 5
(2/3)y = x + 5
y = (3/2)x + (3/2)5
y = 1.5x + 7.5

f⁻¹(x) = 1.5x + 7.5

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

5. f(x) = 2x² - 6

x = 2y² - 6
2y² = x + 6
y² = 1/2x + 3
y = $\sqrt{1/2x + 3}$

f⁻¹(x) = $\sqrt{1/2x + 3}$

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

6. y = (x - 3)²

x = (y - 3)²
$\sqrt{x}$ = y - 3
y = 3 + $\sqrt{x}$

f⁻¹(x) = 3 + $\sqrt{x}$

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4 years ago

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3 years ago

If f(x) =4x^2 + 1 and g(x) =x2 -5, find (f+g)(x)

Lilit [14]

The value of $(f+g)(x)$ is $5 x^{2}-4$

Explanation:

Given that the functions $f(x)=4 x^{2}+1$ and $g(x)=x^{2}-5$

We need to determine the value of $(f+g)(x)$

The value of $(f+g)(x)$ can be determined by substituting the value of $f(x)$ and $g(x)$ and simplifying the terms.

Thus, let us assign $f(x)=4 x^{2}+1$ in the function $(f+g)(x)$ , we have,

$4 x^{2}+1+g(x)$

Now, let us assign $g(x)=x^{2}-5$ in the function $(f+g)(x)$ , we get,

$4 x^{2}+1+x^{2}-5$

Grouping the like terms, we have,

$4 x^{2}+x^{2}+1-5$

Adding the like terms, we get,

$5 x^{2}-4$

Hence, the value of $(f+g)(x)$ is $5 x^{2}-4$

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3 years ago

What is the y-intercept of the linear equation x-1/2 y=-6

Artyom0805 [142]

Answer:

y = 12

Step-by-step explanation:

x - 1/2 y = -6

To find the y intercept set x = 0 and solve for y

0 - 1/2 y = -6

-1/2 y = -6

Multiply each side by -2

-2*-1/2y = -6*-2

y = 12

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3 years ago

Read 2 more answers

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fgiga [73]

Step-by-step explanation:

All these fancy terms is confusing. We just need to substitute the original equations into the final problem statement.

$p(x) = 10x - (8x+40) = 10x - 8x - 40$

We can then substitute 100 for x and solve.

$p(100) = 10(100) - 8(100) - 40$

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3 years ago