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3 years ago

Choose the correct correspondence R OK

Mathematics

1 answer:

harina [27]3 years ago

3 0

What is the question

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Remember to show work and explain. Use the math font.

MrMuchimi

Answer:

$\large\boxed{1.\ f^{-1}(x)=4\log(x\sqrt[4]2)}\\\\\boxed{2.\ f^{-1}(x)=\log(x^5+5)}\\\\\boxed{3.\ f^{-1}(x)=\sqrt{4^{x-1}}}$

Step-by-step explanation:

$\log_ab=c\iff a^c=b\\\\n\log_ab=\log_ab^n\\\\a^{\log_ab}=b\\\\\log_aa^n=n\\\\\log_{10}a=\log a\\=============================$

$1.\\y=\left(\dfrac{5^x}{2}\right)^\frac{1}{4}\\\\\text{Exchange x and y. Solve for y:}\\\\\left(\dfrac{5^y}{2}\right)^\frac{1}{4}=x\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\dfrac{(5^y)^\frac{1}{4}}{2^\frac{1}{4}}=x\qquad\text{multiply both sides by }\ 2^\frac{1}{4}\\\\\left(5^y\right)^\frac{1}{4}=2^\frac{1}{4}x\qquad\text{use}\ (a^n)^m=a^{nm}\\\\5^{\frac{1}{4}y}=2^\frac{1}{4}x\qquad\log_5\ \text{of both sides}$

$\log_55^{\frac{1}{4}y}=\log_5\left(2^\frac{1}{4}x\right)\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\dfrac{1}{4}y=\log(x\sqrt[4]2)\qquad\text{multiply both sides by 4}\\\\y=4\log(x\sqrt[4]2)$

$--------------------------\\2.\\y=(10^x-5)^\frac{1}{5}\\\\\text{Exchange x and y. Solve for y:}\\\\(10^y-5)^\frac{1}{5}=x\qquad\text{5 power of both sides}\\\\\bigg[(10^y-5)^\frac{1}{5}\bigg]^5=x^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(10^y-5)^{\frac{1}{5}\cdot5}=x^5\\\\10^y-5=x^5\qquad\text{add 5 to both sides}\\\\10^y=x^5+5\qquad\log\ \text{of both sides}\\\\\log10^y=\log(x^5+5)\Rightarrow y=\log(x^5+5)$

$--------------------------\\3.\\y=\log_4(4x^2)\\\\\text{Exchange x and y. Solve for y:}\\\\\log_4(4y^2)=x\Rightarrow4^{\log_4(4y^2)}=4^x\\\\4y^2=4^x\qquad\text{divide both sides by 4}\\\\y^2=\dfrac{4^x}{4}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\y^2=4^{x-1}\Rightarrow y=\sqrt{4^{x-1}}$

6 0

4 years ago

Solving Systems Using Inverses

Zanzabum

Answer:

12x the second -12x -16

Step-by-step explanation:

Solving systems of equations with 3 variables is very similar

7 0

3 years ago

4x+3y=23 x-5y=0 using substitution

Andrei [34K]

Answer:

{x,y} = {115/17,-23/17}

Step-by-step explanation:

I believe its true.

8 0

2 years ago

How do the average rates of change for the functions f(x) = 2x2 and g(x) = 3x2 over the interval −3 ≤ x ≤ 4 compare?

DedPeter [7]

<h2>Answer with explanation:</h2>

The average rate of change for function f(x) over the interval a ≤ x ≤ b is given by :-

$\dfrac{f(b)-f(a)}{b-a}$

So, the rate of change for function $f(x)=2x^2$ over the interval −3 ≤ x ≤ 4 :

$=\dfrac{2(4)^2-2(-3)^2}{4-(-3)}=\dfrac{14}{7}=2$

The rate of change for function $g(x)=3x^2$ over the interval −3 ≤ x ≤ 4 :

$=\dfrac{3(4)^2-3(-3)^2}{4-(-3)}=\dfrac{21}{7}=3$

So, the rate of change for g(x) is greater than f(x) over the interval −3 ≤ x ≤ 4.

3 0

3 years ago

A line is imaginary. <br><br> True or False?

Svetradugi [14.3K]

Answer:

The ideal line is a concept. A line that is drawn cannot be a mathematically true line since it will have a thickness - no matter how small. Also, it cannot be infinitely long - no matter how large.

7 0

3 years ago

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Choose the correct correspondence R OK​

Choose the correct correspondence R OK