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Sunny_sXe [5.5K]
3 years ago
9

Determining whether two functions are inverses of each other.

Mathematics
2 answers:
Gnom [1K]3 years ago
8 0

Answer:

f and g are not inverse of each other.

Step-by-step explanation:

If the two functions are inverses of each other, then f(g(x)) = g(f(x))

We are given two functions:

f(x) = 6x + 5

g(x) = 6x - 5

Let's find f(g(x)) and g(f(x))

f(g(x)) = f(6x - 5)

= 6(6x - 5) + 5

= 36x - 30 + 5

f(g(x)) = 36x - 25

Now let's find g(f(x))

g(f(x)) = g(6x + 5)

= 6(6x + 5) - 5

= 36x + 30 - 5

g(f(x))= 36x + 25

We see that f(g(x)) ≠ g(f(x))

Therefore, f and g are not inverse of each other.

murzikaleks [220]3 years ago
4 0
F(x) = 6x + 5
g(x) = 6x - 5
f(g(x)) = 6(6x - 5) + 5 = 36x - 30 + 5 = 36x - 25
g(f(x)) = 6(6x+ 5) - 5 = 36x + 30 - 5 = 36x + 25

f and g are not inverse of each other.
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The rectangular field is 120 yards long and 40 yards wide. How many square yards is it’s area?
lilavasa [31]

Answer:

4800 yards wide

Step-by-step explanation:

120 x 40=4800

3 0
3 years ago
SU and VT are chords that intersect at point R.
vovikov84 [41]

Answer:

<h2>The length of the line segment VT is 13 units.</h2>

Step-by-step explanation:

We know that SU and VT are chords. If the intersect at point R, we can define the following proportion

\frac{RS}{RT} =\frac{RV}{RU}

Where

RS=SR=x+6\\RT=x+4\\VR=RV=x+1\\RU=x

Replacing all these expressions, we have

\frac{x+6}{x+4} =\frac{x+1}{x}

Solving for x, we have

x(x+6)=(x+4)(x+1)\\x^{2} +6x=x^{2} +x+4x+4\\6x-5x=4\\x=4

Now, notice that chord VT is form by the sum of RT and RV, so

VT=VR+RT\\VT=x+1+x+4\\VT=2x+5

Replacing the value of the variable

VT=2(4)+5\\VT=8+5\\VT=13

Therefore, the length of the line segment VT is 13 units.

5 0
3 years ago
Read 2 more answers
Write an expression for 5 times the difference of twice a number and 4
777dan777 [17]

Answer:

1. 50-x

2. 2x+189

3. x+109

4. x+99

5. x*(76-39)

6. 75+x

7. 45-3x

8. 2x+15

9. 3x-25

10. x*(x+88)

Step-by-step explanation:

4 0
2 years ago
Graph y=x+1/x² and y=1/x for positive values of x.
AlekseyPX

Answer:

Graphic is showed in the figure below

Step-by-step explanation:

To graph the equations given, let's do a table for positive values of x, and, by replacing it in the equation, let's calculate the value of y. Knowing the coordinate points (x,y) we can build the graphic.

<em>x        y= x + 1/x²       y = 1/x</em>

1             2                    1

2          2.25               0.2

3          3.11                 0.33

4          4.06               0.25

When x->0 both equations -> ∞, because lim(1/x) x->0 = ∞

The graphic is showed below. In red there is y = 1 + 1/x² and in blue y = 1/x

6 0
3 years ago
Evaluate f(x)=5•3 ( to the power of x) for x=4
GenaCL600 [577]
The answer is 50625 because 5*3 is 15 and take that to the power of 4
5 0
3 years ago
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