All categories

3 years ago

If f(x) = x^2 -1, what is the equation for f–1(x)?

Mathematics

2 answers:

schepotkina [342]3 years ago

5 0

Answer:

The inverse is ±sqrt(x+1)

Step-by-step explanation:

y = x^2 -1

Exchange x and y

x = y^2 -1

Solve for y

Add 1 for each side

x+1 = y^2-1+1

x+1 = y^2

Take the square root of each side

±sqrt(x+1) = sqrt(y^2)

±sqrt(x+1) = y

The inverse is ±sqrt(x+1)

sweet [91]3 years ago

5 0

Answer:

f^-1(x) = sqrt(x + 1)

f^-1(x) = -sqrt(x + 1)

Step-by-step explanation:

y = x² - 1

x² = y + 1

x = +/- sqrt(y + 1)

Interswitch variables:

f^-1(x) = sqrt(x + 1)

f^-1(x) = -sqrt(x + 1)

Where sqrt: square root

You might be interested in

Which value represents the horizontal translation from the graph of the parent function f(x) = x^2 to the graph of the function

Vsevolod [243]

Translation by h (right) and k (up)
g(x)=f(x-h)+k
=f(x-4)^2+2
so h=4, k=2
horizontal translation (to the right) is h=+4, but is shown as -4 for the translation value.

7 0

3 years ago

Find the value of y.y^2=169

wel

y^2=169

y = √169

y = + / - 13

Answer

y = -13 or y = 13

8 0

3 years ago

Write an equation for the line, given that m= 0 and the y - intercept (0, -2)

stich3 [128]

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

so...

m = 0

b = -2

^^^Plug these numbers into formula

y = 0*x - 2

y = 0 - 2

y = -2

Hope this helped!

~Just a girl in love with Shawn Mendes

3 0

3 years ago

Read 2 more answers

Anyone have the answer for this

sergiy2304 [10]

$\huge\bold{Given:}$

Length of the base = 16 km.

Length of the hypotenuse = 34 km. $\huge\bold{To\:find:}$

✎ The length of the missing leg '' $a$ ".

$\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}$

The length of the missing leg "a" is $\boxed{30\:km}$ .

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}$

Using Pythagoras theorem, we have

$({perpendicular})^{2} + ({base})^{2} = ({hypotenuse})^{2} \\ ⇢ {a}^{2} + ({16 \: km})^{2} = ({34 \: km})^{2} \\ ⇢ {a}^{2} + 256 \: {km}^{2} = 1156 \: {km}^{2} \\ ⇢ {a}^{2} = 1156 \: {km}^{2} - 256 \: {km}^{2} \\ ⇢ {a}^{2} = 900 \: {km}^{2} \\ ⇢a \: = \sqrt{900 \: {km}^{2} } \\ ⇢a = \sqrt{30 \times 30 \: {km}^{2} } \\ ⇢a = 30 \: km$

$\sf\blue{Therefore,\:the\:length\:of\:the\:missing\:leg\:"a"\:is\:30\:km.}$

$\huge\bold{To\:verify :}$

$( {30 \: km})^{2} + ({16 \: km})^{2} =( {34 \: km})^{2} \\ ⇝900 \: {km}^{2} + 256 \: {km}^{2} = 1156 \: {km}^{2} \\⇝1156 \: {km}^{2} = 1156 \: {km}^{2} \\ ⇝L.H.S.=R. H. S$

Hence verified. ✔

$\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘$

7 0

2 years ago

What is 4x-8y=5 6x-12y=10

Anvisha [2.4K]

If it is a system of two unknowns:
1) 4x-8y=5 multiple by 3
2)6x-12y=10 multiple by -2
then
12x-24y=15
-12x+24y=-20
x and y equals 0, so
Answer: no solution

5 0

3 years ago