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ratelena [41]
3 years ago
11

If f(x) = x + 4 and g(x)=x^2-1, what is m(g o f)(x)?

Mathematics
2 answers:
Andreas93 [3]3 years ago
8 0

Until now, given a function  f(x), you would plug a number or another variable in for x. You could even get fancy and plug in an entire expression for x. For example, given  f(x) = 2x + 3, you could find f(y2 – 1) by plugging y2 – 1 in for x to get f(y2 – 1) = 2(y2 – 1) + 3 = 2y2 – 2 + 3 = 2y2 + 1.

In function composition, you're plugging entire functions in for the x. In other words, you're always getting "fancy". But let's start simple. Instead of dealing with functions as formulas, let's deal with functions as sets of (x, y) points:

Let f = {(–2, 3), (–1, 1), (0, 0), (1, –1), (2, –3)} and  

let g = {(–3, 1), (–1, –2), (0, 2), (2, 2), (3, 1)}.  

 

Find (i) f (1), (ii) g(–1), and (iii) (g o f )(1).

(i) This type of  exercise is meant to emphasize that the (x, y) points are really (x, f (x)) points. To find  f (1), I need to find the (x, y) point in the set of (x, f (x)) points that has a first coordinate of x = 1. Then f (1) is the y-value of that point. In this case, the point with x = 1 is (1, –1), so:

ruslelena [56]3 years ago
5 0

Answer:

gof(x) = x²+8x+15

Step-by-step explanation:

gof(x) = g(f(x))

f(x) = x + 4 and g(x)=x²-1

Substituting

     gof(x) = g(f(x)) = g(x + 4) = (x+4)²-1

       gof(x) = x²+8x+16 -1 = x²+8x+15

That is if f(x) = x + 4 and g(x)=x²-1, gof(x) = x²+8x+15

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Which equation has a solution of x = -17
Agata [3.3K]

Answer is (d) -4x = 68

Solving it we get :

-4x = 68

x = -68/4 = -17

8 0
3 years ago
What is the slope of the line through the point (-4,6) and (-3,-1)?
zimovet [89]

Answer:

B.) -7/1

Step-by-step explanation:

Finding the slope we use: y2 - y1/x2 - x1

m = -1 - 6/-3 - (-4)

m = -7/-3 + 4

m = -7/1

4 0
3 years ago
A cone has the diameter of 15 inches and is 27 inches tall what is the volume for the cone?
suter [353]

Answer:

the volume of a cone = 1589.625feet³

Step-by-step explanation:

given that the diameter of the cone = 15inches

radius = 15inches/2 = 7.5inches

height of the cone = 27 inches

volume of the cone = ?

recall that

the  formulae for finding the volume of a cone is given to be

= 1/3πr²h

the volume of a cone = πr² h/3

the volume of a cone = 3.14  × ( 7.5)² × 27/3

the volume of a cone = (3.14 x  56.25 x27)/3

the volume of a cone = 4768.875/3

the volume of a cone = 1589.625feet³

6 0
3 years ago
Mobile phone calls are charged at 17 cents per 30 seconds.
vovikov84 [41]

0.17/30 = x/450 <em>Use proportion</em>

76.50 = 30x <em>Cross multiply</em>

2.55 = x <em>Divide 30 both sides</em>

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7.5 minutes call would cost 2.55

7 0
3 years ago
Read 2 more answers
Test the claim that the proportion of people who own cats is significantly different than 90% at the 0.1 significance level.
miss Akunina [59]

Answer:

The right answer is Option B:

H_0: \pi=0.9\\\\H_1: \pi\neq0.9

Step-by-step explanation:

In this case we have to perform a hypothesis test on the proportion of the people owning cats.

The claim is that the proportion is significantly different than 905, what means it can be greater or smaller than 90% to reject the null hypothesis. Because of that, the null hypothesis has to state an equality (H0:p=0.9).

The right answer is Option B:

H_0: \pi=0.9\\\\H_1: \pi\neq0.9

4 0
2 years ago
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