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2 years ago

I need help with this question

Mathematics

1 answer:

Cloud [144]2 years ago

4 0

Answer: given and explained briefly below.

In these questions, we go right to left of the function to solve.

(a)

given that

f(x) = x - 3

g(x) = x + 3

(i) fg(x)

= f(x + 3)

= ( x +3 ) -3

= x

(ii) gf(x)

= g(x-3)

= (x-3)+3

= x

to find inverse, we have to make x the subject,

f(x) = x - 3

f(x) + 3 =x

f^-1(x) = x + 3

g(x) = x + 3

g(x) -3 = x

g^-1(x) = x -3

f and g are inverses of each other

(b)

given that

f(x) = -1/4x

g(x) = 1/4x

fg(x) =

f(1/4x)

1/4(-1/4x)

= x

gf(x)

g(-1/4x)

-1/4(1/4x)

= -x

to find inverse, we have to make x the subject,

f(x) = -1/4x

-1/f(x) = 4x

f^-1(x) = -1/4x

g(x) = 1/4x

x = 1/4g(x)

g^-1(x) = 1/4x

f and g are not inverses of each other here.

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4 years ago

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3 years ago

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Rudik [331]

Answer:

x = 2

Step-by-step explanation:

First translate the image into an equation using the key. Once you do that, your equation should look like this:

(x + x + x) + (-1 + -1 + -1 + -1 + -1) = (-x + -x) + (1 + 1 + 1 + 1 + 1)

________________________________

3x - 5 = -2x + 5

(given)

________________________________

3x - 5 = -2x + 5

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(addition property of equality)

*cancel out -5 on the left hand side, and isolate it from x by adding +5 on each side*

__________________________

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+2x +2x

(addition property of equality)

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If you want to test this solution, substitute this back into the equation.

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3 years ago

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Alla [95]

Answer:

Labelled the given figure triangle as A, B and C.

In triangle ABC;

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A = (0, 4)

B = (-2, 10) and

C = (-6, 8)

To find the image of this figure after a dilation with a scale factor of $\frac{1}{2}$ centered at the point O=(2, 2).

The rule of dilation with scale factor $\frac{1}{2}$ centered at the point (2, 2) is given by;

$(x, y) \rightarrow (\frac{1}{2}(x-2) +2 , \frac{1}{2}(y-2) +2)$

$(x, y) \rightarrow (\frac{1}{2}x+1 , \frac{1}{2}y+1)$

The coordinate of the image of the figure after dilation are;

$A(0, 4) \rightarrow A'(\frac{1}{2}(0)+1 , \frac{1}{2}(4)+1)$ = A'(1, 3)

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You can see the graph as shown below in the attachment:

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