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Strike441 [17]
3 years ago
14

Which points are on the graph of the function rule f(x) = 10 – 4x?

Mathematics
2 answers:
kondor19780726 [428]3 years ago
8 0
(–2, 18), (0, 10), (2, 2)
FromTheMoon [43]3 years ago
4 0

Answer with Step-by-step explanation:

we are given that:

f(x)=10-4x

We have to determine which points lie on the graph of f(x)

1. (2, –18), (0, –10), (–2, –2)

When x=0

f(x)=10

But here we are given (0,-10)

Hence, this option is incorrect

2. (18, –2), (10, 0), (2, 2)

When x=10

f(x)= -30

but here we are given (10,0)

Hence, this option is incorrect

3. (–18, 2), (–10, 0), (–2, –2)

when x= -10

f(x)= 50

but here we are given (-10,0)

Hence, this option is incorrect

4. (–2, 18), (0, 10), (2, 2)

f(-2)=18,f(0)=10 and f(2)=2

Hence, Correct option is:

(–2, 18), (0, 10), (2, 2)

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The domain and target set of functions f and g isR. The functions are definedas:(b)•f(x) = 2x+ 3•g(x) = 5x+ 7(a)f◦g?(b)g◦f?(c) (
adoni [48]

Answer:

Step-by-step explanation:

Given the domain and target set of functions f and g expressed as;

f(x) = 2x+3 an g(x) = 5x+7 we are to find the following;

a) f◦g

f◦g = f[g(x)]

f[g(x)] = f[5x+7]

To get f(5x+7), we will replace the variable x in f(x) with 5x+7 as shown;

f(x) = 2x+3

f(5x+7) = 2(5x+7)+3

f(5x+7) = 10x+14+3

f(5x+7) = 10x+17

Hence f◦g = 10x+17

b) g◦f

g◦f = g[f(x)]

g[f(x)] = g[2x+3]

To get g(2x+3), we will replace the variable x in g(x) with 2x+3 as shown;

g(x) = 5x+7

g(2x+3) = 5(2x+3)+7

g(2x+3) = 10x+15+7

g(2x+3) = 10x+22

Hence g◦f = 10x+22

c) For (f◦g)−1 (inverse of (f◦g))

Given (f◦g) = 10x+17

To find the inverse, first we will replace (f◦g) with variable y to have;

y = 10x+17

Then we will interchange variable y for x:

x = 10y+17

We will then make y the subject of the formula;

10y = x-17

y = x-17/10

Hence the inverse of the function

(f◦g)−1 = (x-17)/10

d) For the function f−1◦g−1

We need to get the inverse of function f(x) and g(x) first.

For f-1(x):

Given f(x)= 2x+3

To find the inverse, first we will replace f(x) with variable y to have;

y = 2x+3

Then we will interchange variable y for x:

x = 2y+3

We will then make y the subject of the formula;

2y = x-3

y = x-3/2

Hence the inverse of the function

f-1(x) = (x-3)/2

For g-1(x):

Given g(x)= 5x+7

To find the inverse, first we will replace g(x) with variable y to have;

y = 5x+7

Then we will interchange variable y for x:

x = 5y+7

We will then make y the subject of the formula;

5y = x-7

y = x-7/5

Hence the inverse of the function

g-1(x) = (x-7)/5

Now to get )f−1◦g−1

f−1◦g−1 = f-1[g-1(x)]

f-1[g-1(x)] = f-1(x-7/5)

Since f-1(x) = x-3/2

f-1(x-7/5) = [(x-7/5)-3]/2

= [(x-7)-15/5]/2

= [(x-7-15)/5]/2

= [x-22/5]/2

= (x-22)/10

Hence f−1◦g−1 = (x-22)/10

e) For the composite function g−1◦f−1

g−1◦f−1 = g-1[f-1(x)]

g-1[f-1(x)] = g-1(x-3/2)

Since g-1(x) = x-7/5

g-1(x-3/2) = [(x-3/2)-7]/5

= [(x-3)-14)/2]/5

= [(x-17)/2]/5

= x-17/10

Hence g-1◦f-1 = (x-17)/10

5 0
3 years ago
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