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3 years ago

Consider function f. f(x) = sqrt 7x- 21

Mathematics

2 answers:

Arada [10]3 years ago

6 0

Answer:

f^-1(x) = (x² + 21)/7

Step-by-step explanation:

Since f(x) = y = √(7x – 21), to find the inverse of f(x) we have to write x in terms of y in order to make x the dependent variable and y the independent variable. The steps involved are:

Step 1: square both sides of the equation, y = √(7x – 21). Doing that, we have:

y² = 7x – 21

Step 2: Add 21 to both sides of the resulting equation. Doing that, we have:

y² + 21 = 7x

Step 3: Divide both sides of the equation by 7. Doing that we have:

x = (y² + 21)/7

Step 4: Replace x with f^-1(x) and y with x. Doing that, we have:

f^-1(x) = (x² + 21)/7

kipiarov [429]3 years ago

4 0

Answer:look at explanation

Step-by-step explanation:

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Meenu bought two fans for ₹1200 each. She sold one at a loss of 5% and the other at a profit of 10%. Find the selling price of e

Vinvika [58]

<h3><u>Solution: </u></h3>

Overall<u> </u>CP of each fan = ₹1200 .

One is sold at a loss of 5% .

( This means if CP is ₹100, SP is ₹95 ) .

• Therefore,When CP is ₹1200 , Then SP is ₹ 1140.

$= > \frac{95}{100} \times 1200 = 1140$

Also,Second fan is sold at a profit of 10% .

It means , If CP is ₹100 , SP is ₹110.

Therefore , When CP is ₹1200 , Then SP is ₹1320.

<u>• We need to find the combined CP and SP to say whether there was an overall profit or Loss.</u><u>.</u>

Total CP = ₹ 1200 + ₹ 1200 = ₹ 2400.
Total SP = ₹ 1140 + ₹ 1320 = ₹ 2460.

Since total SP > total CP , A profit of ₹ ( 2460 - 2400 ) or ₹60 has been made ..

<h3>Hope this helps you :)</h3>

4 0

3 years ago

How could i write 2.7 on a number line?

Viefleur [7K]

There tried too draw it out of you

3 0

3 years ago

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:

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

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

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

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

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