Given that g(x)= 2x+1/5 and f(x)=x+4
Calculate the value of g(-2)
2(-2)+1/5= -3/5
Is this right??
How do i write an expression for gf(x) in the simpliest form??
And how do i find inverse functions such as g`1(x)?
g(x) = 2x+1/5
Substitute -2 for x.
g(-2) = 2*-2 + 1/5
g(-2) = -4 + 1/5
g(-2) = (-3 4/5) (mixed number)
To find g(f(x)), substitute f(x) for x in g.
g(f(x)) = g(x+4)
g(x+4) = 2(x+4) + 1/5
g(x+4) = 2x + 8 + 1/5
g(x+4) = 2x + (8 1/5) (mixed number)
To find inverse functions, switch the y and x.
convert g(x) = 2x+1/5 to y = 2x+1/5
Now switch y and x.
x = 2y+1/5
solve for y
x-1/5 = 2y
x/2 - 1/10 = y
g'1(x) = x/2 - 1/10
for the #1 how do u got -3 4/5 if u check good u got -3/5
To find the value of g(-2), you substitute -2 into the expression for g(x):
g(-2) = 2(-2) + 1/5
= -4 + 1/5
= -4 + 0.2
= -3.8
So the correct value of g(-2) is -3.8, not -3/5.
To find the expression for gf(x), you substitute f(x) into the expression for g(x):
gf(x) = g(f(x))
= g(x + 4)
= 2(x + 4) + 1/5
= 2x + 8 + 1/5
= 2x + 41/5
To find the inverse function g^(-1)(x), you follow these steps:
1. Replace g(x) with y: y = 2x + 1/5.
2. Swap x and y: x = 2y + 1/5.
3. Solve for y: x - 1/5 = 2y.
4. Divide both sides by 2: (x - 1/5)/2 = y.
5. Replace y with g^(-1)(x): g^(-1)(x) = (x - 1/5)/2.
So, the expression for the inverse function g^(-1)(x) is (x - 1/5)/2.
To calculate the value of g(-2), you substitute x = -2 into the equation g(x) = 2x + 1/5:
g(-2) = 2(-2) + 1/5
= -4 + 1/5
= -4 + 0.2
= -3.8
So, the correct value of g(-2) is -3.8, not -3/5.
To write an expression for gf(x) in the simplest form, you need to substitute g(x) into f(x).
gf(x) = g(f(x))
= g(x + 4)
To simplify this expression, you can expand g(x + 4) by substituting (x + 4) into the equation g(x):
gf(x) = 2(x + 4) + 1/5
= 2x + 8 + 1/5
= 2x + 8 + 0.2
= 2x + 8.2
Therefore, the simplest form of gf(x) is 2x + 8.2.
To find the inverse function of g(x), denoted as g^(-1)(x), you need to swap the positions of x and y in the equation g(x) = 2x + 1/5 and solve for y:
y = 2x + 1/5
Interchanging x and y, we get:
x = 2y + 1/5
Now, solve this equation for y to find g^(-1)(x):
x - 1/5 = 2y
2y = x - 1/5
y = (x - 1/5) / 2
Therefore, g^(-1)(x) = (x - 1/5) / 2.