All categories

3 years ago

Find the inverse of f(x)=5x-2

Mathematics

1 answer:

kompoz [17]3 years ago

5 0

Answer:

$f^{-1}$ (x) = $\frac{x+2}{5}$

Step-by-step explanation:

Let y = f(x) and rearrange making x the subject

y = 5x - 2 ( add 2 to both sides )

y + 2 = 5x ( divide both sides by 5 )

$\frac{y+2}{5}$ = x

Change y back into terms of x

$f^{-1}$ (x) = $\frac{x+2}{5}$

You might be interested in

If RS=ST then Point S Is Called The Midpoint Of

madam [21]

Answer: always

Hope i helped :)

6 0

3 years ago

Read 2 more answers

Which statement is true regarding the graphed functions?

algol13

Answer:

x--5-4-3-2-1

Step-by-step explanation:

because it is x axis not y axis

8 0

3 years ago

For a school fundraiser, Mai will make school spirit bracelets. She will order bead wiring and alphabet beads to create the scho

Ket [755]

Answer: Total number of bracelet: 235

Step-by-step explanation:

Given:

Total budget= $1,500

Spend on wire = $250

Per braclet beads = $5.30

Find:

Total number of bracelet

Computation:

Total number of bracelet = [1,500 - 250]

Total number of bracelet = [1,250/ 5.30

Total number of bracelet = 235.849

Total number of bracelet = 235 [By round minium]

8 0

3 years ago

Every year on Earth Day, a group of volunteers pick up garbage at Hidden Falls Park. The time takes to clean the beach varies in

KengaRu [80]

Answer:

Step-by-step explanation:

8 0

3 years ago

Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
$f_x=5yz=0\implies y=0\text{ or }z=0$
$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
$L_z=5xy+2\lambda z=0$
$L_\lambda=x^2+y^2+z^2-1=0$

We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

5 0

3 years ago