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GenaCL600 [577]
2 years ago
14

If ƒ(x ) = 3x + 1 and ƒ -1 = , then ƒ -1(7) =

Mathematics
1 answer:
Elden [556K]2 years ago
6 0
F(x) = 3x + 1

let f(x) = y

y = 3x + 1

y - 1 = 3x

3x = y - 1

x = (y - 1)/3

From y = f(x),  x = f⁻¹(y) 

<span>x = (y - 1)/3
</span>
 f⁻¹(y)  = (y - 1)/3

f⁻¹(7)  = <span>(7 - 1)/3 = 6/3 = 2

</span>f⁻¹(7)<span> = 2</span>
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Find the measure of the the sides of DEF then classify it by it sides. <br> D(8,-6) E(-1,-3) F(-2,5)
Mama L [17]

Answer:

Part a) The measure of the sides of triangle DEF are

d_D_E=\sqrt{90}\ units

d_E_F=\sqrt{65}\ units

d_D_F=\sqrt{221}\ units

Part b) Is a scalene triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have the coordinates

D(8,-6) E(-1,-3) F(-2,5)

step 1

Find the length side DE

D(8,-6) E(-1,-3)

substitute in the formula

d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}

d=\sqrt{(3)^{2}+(9)^{2}}

d_D_E=\sqrt{90}\ units

step 2

Find the length side EF

E(-1,-3) F(-2,5)

substitute in the formula

d=\sqrt{(5+3)^{2}+(-2+1)^{2}}

d=\sqrt{(8)^{2}+(-1)^{2}}

d_E_F=\sqrt{65}\ units

step 3

Find the length side DF

D(8,-6) F(-2,5)

substitute in the formula

d=\sqrt{(5+6)^{2}+(-2-8)^{2}}

d=\sqrt{(11)^{2}+(-10)^{2}}

d_D_F=\sqrt{221}\ units

step 4

Classify the triangle by the measure of its sides

we have

d_D_E=\sqrt{90}\ units

d_E_F=\sqrt{65}\ units

d_D_F=\sqrt{221}\ units

so

Is a scalene triangle, because is a triangle in which all three sides have different lengths.

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