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blagie [28]
3 years ago
10

If the function f(x)=mx+b has an inverse function, which statement must be true

Mathematics
2 answers:
PIT_PIT [208]3 years ago
3 0

Answer:

The first option .

Step-by-step explanation:

m must not be zero

Anna71 [15]3 years ago
3 0

Answer:

a) m ≠ 0

Step-by-step explanation:

Given: The function y = mx + b has an inverse function.

The given function is the equation of a line in slope-intercept form.

m is the slope and y-intercept is b.

Given that the function has an inverse function, therefore, the slope must not be equal to zero.

What if the slope is zero, if the slope is zero, then there will not be an inverse function.

Therefore, the answer is m≠ 0.

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4 0
3 years ago
A cone has radius 9 and a height 12. A frustum of this cone has height 4.
Anettt [7]

Answer:

Part A)

The lower base has a radius of 9 units, and the upper base has a radius of 6 units.

Part B)

5 units.

Part C)

75π or about 235.62 square units.

Step-by-step explanation:

Please refer to the figure below.

The cone has a radius of 9 units and a total height of 12 units.

A frustum of the cone has a height of 4 units.

Part A)

The lower radius of the frustum will simply be 9 units.

For the upper radius, we will use the properties of similar triangles. We will compare the smaller upper triangle to the overall larger triangle. This yields:

\displaystyle \frac{12}{8}=\frac{9}{x}

Solve for <em>x.</em> Simplify:

\displaystyle \frac{3}{2}=\frac{9}{x}

Cross-multiply:

18=3x\Rightarrow x=6

The upper base has a radius of 6 units.

Part B)

We can first find the total slant height of the entire cone. By using the Pythagorean Theorem, this yields that the total slant height is:

SH^2=12^2+9^2

Simplify:

SH^2=225\Rightarrow SH=15\text{ units}

Now, find the slant height of the upper cone:

(SH_\text{cone})^2=8^2+6^2=100

So:

SH_\text{cone}=10

Then the slant height of the frustum will be the cone subtracted from the total. Thus:

SH_{\text{frustum}}=15-10=5\text{ units}

Part C)

We can first find the lateral area of the entire cone. The lateral area is given by:

LA=\pi r\ell

The lateral area of the entire cone will be:

LA=\pi (9)(15)=135\pi

The lateral area of the upper cone will be:

LA_\text{cone}=\pi(6)(10)=60\pi

Then the lateral area of the frustum is:

LA_\text{frustum}=135\pi-60\pi =75\pi\text{ units}^2\approx235.62\text{ units}^2

5 0
2 years ago
F(x)= -7x-1<br> f(_)=-8<br><br> Please help.. ASAP!
navik [9.2K]

-8=-7x -1

Add 1 to both sides

-7=-7x

Divide both sides by -7

X=1

4 0
3 years ago
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