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hjlf
2 years ago
11

Question 19 of 25 f(x)=√x-6. Find the inverse of f(x) and its domain.

Mathematics
1 answer:
Gekata [30.6K]2 years ago
5 0

Answer:

f¯¹(x)=x²+12x+36

Step-by-step explanation:

f(x) =  \sqrt{x}  - 6 \\ substitute \: y \: for \: f {}^{ - 1} (x) \\ y =  \sqrt{x}  - 6 \\ interchange \: x \: and \: y \\ x =  \sqrt{y}  - 6 \\ swap \: the \: side \: of \: the \: equation \\  \sqrt{y }  - 6 = x \\ move \: the \: constant \: to \: the \: right \: hand \: side \\   \sqrt{y}  = x + 6 \\ square \: both \: sides \: of \: the \: equation \\ y = x {}^{2}  + 12x + 36 \\ substitute \: f \frac{}{ -1} (x) \: for \: y \\ f {}^{ - 1} (x) = x {}^{2}  + 12x + 36 \\ domain \: x∈R

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What is the sum of the expressions for n=-2n=−2 and m=5m=5 ?
Liula [17]

Answer:

- 43

Step-by-step explanation:

Expression: (3m+2n−6) and (−4−6m+7n)

n= -2 and m=5

Before inserting the values, let's add both expressions.

(3m+2n−6)  + (−4−6m+7n)

3m+2n−6   −4 − 6m + 7n

-3m + 9n - 10

Inserting the values;

-3(5) + 9(-2) - 10

-15 - 18 -10

- 43

6 0
3 years ago
If f(x)=x*−81 and g(x)=(x−9)−1(x+9), find g(x)×f(x).
Nostrana [21]
F(x) = x²-81

g(x) = (x-9) -1(x+9)

= (x-9) -x-9


g(x) • f(x)



= [x²-81 ] • [ (x-9) -x-9 ]

=[ x²-81 ] • [ (x-x -9-9) ]
= [ x²-81 ] •[0-18]
= [ x²-81] •[ -18]

= -18•x² +-81•-18
= -18x²+1458
7 0
3 years ago
Evaluate the expression 3(x - 1)' + 2x - 7 for = 3,
Marizza181 [45]

Answer and step-by-step explanation:

Break the bracket out would be the first step to evaluate this expression:

3(x-1)

= 3x - 3

Hope this helped :3

4 0
4 years ago
Which axiom is used to prove that the product of two rational numbers is rational
aliina [53]

Answer:

First, a rational number is defined as the quotient between two integer numbers, such that:

N = a/b

where a and b are integers.

Now, the axiom that we need to use is:

"The integers are closed under the multiplication".

this says that if we have two integers, x and y, their product is also an integer:

if x, y ∈ Z ⇒ x*y ∈ Z

So, if now we have two rational numbers:

a/b and c/d

where a, b, c, and d ∈ Z

then the product of those two can be written as:

(a/b)*(c/d) = (a*c)/(b*d)

And by the previous axiom, we know that a*c is an integer and b*d is also an integer, then:

(a*c)/(b*d)

is the quotient between two integers, then this is a rational number.

5 0
3 years ago
What is 5/8 ± 2/5? Please Help easy points
Sphinxa [80]
Easy points thank you so much :^)

4 0
3 years ago
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