Find the inverse function of : f(x)=2x-6.f(x)=2x−6.

2 answers:

7 0

$FUNCTIONS \\ \\ \\ To \: find \: the \: inverse \: , \: replace \: \\ f(x) \: with \: y . \\ \\ \: f(x) = 2x - 6 \\ \: \: \: \: \: \: \: \: \: y \: = \: 2x - 6 \\ \\ \: \: Interchange \: the \: variables \\ \: \: \: \: \: \: \: \: \: x = 2y - 6 \\ \\ \: \: \: \: \: \: \: \: \: Solve \: for \: y \: \\ \: \: \: \: \: \: \: \: y \: \: = \: 3 + \frac{x}{2} \\ \\ {f}^{ - 1} (x) = 3 + \frac{x}{2 }$

mihalych1998 [28]3 years ago

6 0

$\displaystyle f(x) = 2x - 6 \iff y = 2x - 6 \implies x = 2y - 6 \implies x+ 6 = 2y \implies \\ \\
y = \frac{1}{2}x + 3 \implies \bf f^{-1}(x) = \frac{1}{2}x + 3$

You might be interested in

Think of a number, double the number,

Rashid [163]

Answer:

Let x be the number

double x = 2 x

square the result (2x)^2

(2x)^2 - x subtract the original number

4 x^2 - x = 33

4 x^2 - x - 33 = 0

Solve the quadratic

(1 +- (1 + 4 * 132)^1/2) / 8

= (1 + 528^1/2) / 8 = (1 + 23) / 8 = 3 using the positive exponent

Check:

(2 * 3)^2 - 3 = 36 - 3 = 33

5 0

2 years ago

Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic (debit and credit) cards in making purchases (A

umka2103 [35]

Answer:

Given the consumer is 18 to 24 years old, there is 37% probability that he uses a plastic card.

Step-by-step explanation:

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

In this problem, we have:

What is the probability of the consumer using a plastic card, given that the consumer is 18 to 24 years old.

The problem states that the probability that a consumer uses a plastic card when making a purchase is .37, so $P(B) = 0.37$

P(A/B) is the probability that the consumer being 18 to 24 years old, given that he uses a plastic card. The problem states that this probability is .19. So $P(A/B) = 0.19$

P(A) is the probability that the consumer is 18 to 24 years old. There is a .81 probability that the consumer is more than 24 years old. So there is a .19 probability that he is 18 to 24 years old. So $P(A) = 0.19$