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2 years ago

Consider the combined function. f(X) + g(X) = 9x + 4 . If f(x) = 4x - 3, find g(x)

Mathematics

1 answer:

Amanda [17]2 years ago

6 0

Answer:

g(x)=5x+7

Step-by-step explanation:

f(x)+g(x)=9x+4

We are given f(x)=4x-3.

So we insert 4x-3 for f:

4x-3+g(x)=9x+4

Subtract 4x on both sides:

-3+g(x)=5x+4

Add 3 on both sides:

g(x)=5x+7

Check:

f(x)+g(x)

=(4x-3)+(5x+7)

=(4x+5x)+(-3+7)

=(9x) +(4)

=9x+4

Bingo. We did it! :)

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Which describes the behavior of the function f(x)= tan^-1(x)?

Fantom [35]

Answer:

Third Option

Step-by-step explanation:

We know that the function $tan(x)$ is defined as $y=\frac{sin(x)}{cos(x)}$ . Since the denominator is $cos(x)$ then we know that $cos(x)=0$ when $x=\frac{\pi}{2}$

We also know that the division by 0 is not defined. Therefore, the limit of $y=tan(x)$ when "x" tends to $\frac{\pi}{2}$ is infinite.

The function $tan^{-1}(x)$ is the inverse of $tan(x)$

By definition, if we have a function f(x), its domain will be equal to the range of its inverse function $f^{-1}(x)$ . If $f(3)=8$ , then $f^{-1}(8)=3$

This also happens for the function $tan^{-1}(x)$

If when $x \to \frac{\pi}{2}, tan(x) \to \infty$ then when $x \to \infty, tan^{-1}x \to \frac{\pi}{2}$

Then, the answer is:

$x \to \infty, f(x) \to \frac{\pi}{2}$

7 0

2 years ago

Divide 5 in a ratio of 1:2:3

anastassius [24]

In plain and short, we simply divide 5 by (1+2+3) and then distribute the pieces likewise

$\bf 5\qquad 1:2:3\qquad \cfrac{5}{1+2+3}\implies \cfrac{5}{6}
\\\\\\
\stackrel{\textit{ratio of 1}}{1\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 2}}{2\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 3}}{3\left( \frac{5}{6} \right)}\qquad \implies \qquad \frac{5}{6}~:~\frac{5}{3}~:~\frac{5}{2}$

add the ratios up, and you'll get 5.

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2 years ago

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lidiya [134]

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6 0

2 years ago

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dlinn [17]

Answer:

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Step-by-step explanation:

-4(5p+3)

by opening brackets, you get

-20p -12

3 0

2 years ago

1/4-5/8n is equivalent to p(2-5n)

jolli1 [7]

Answer:

1/4 - 5/8n = p (2-5n)

7 0

2 years ago

Read 2 more answers