Find a. fog
b. gof
c. fof
d. gog
for each function
f(x)=4-x
g(x)=3x-5
I will do one,
b)
gof
= g(f(x)
= g(4-x)
= 3(4-x) - 5 = 12- 3x - 5
= 7 - 3x
try the others in the same way
given:f(x)=3x-5,g(x)=x2, find f o g?
Fog=9-3x
Hello mayjoy your answer for finding fog is 6x-15
To find the values for each function composition, we need to substitute one function into another and simplify the expression. Let's go through each function composition:
a. fog (f circle g):
To find fog(x), we need to substitute g(x) into f(x). So we replace x in f(x) with g(x):
fog(x) = f(g(x))
Since g(x) = 3x - 5, we substitute it into f(x):
fog(x) = f(3x - 5)
Now, we substitute f(x) = 4 - x into the above expression:
fog(x) = 4 - (3x - 5)
Simplifying the expression gives:
fog(x) = 9 - 3x
So, fog(x) = 9 - 3x.
b. gof (g circle f):
To find gof(x), we need to substitute f(x) into g(x). So we replace x in g(x) with f(x):
gof(x) = g(f(x))
Since f(x) = 4 - x, we substitute it into g(x):
gof(x) = g(4 - x)
Now, we substitute g(x) = 3x - 5 into the above expression:
gof(x) = 3(4 - x) - 5
Simplifying the expression gives:
gof(x) = 12 - 3x - 5
Combining like terms gives:
gof(x) = 7 - 3x
So, gof(x) = 7 - 3x.
c. fof (f circle f):
To find fof(x), we need to substitute f(x) into f(x). So we replace x in f(x) with f(x):
fof(x) = f(f(x))
Since f(x) = 4 - x, we substitute it into f(x):
fof(x) = f(4 - x)
Now, we substitute f(x) = 4 - x into the above expression:
fof(x) = 4 - (4 - x)
Simplifying the expression gives:
fof(x) = 4 - 4 + x
Combining like terms gives:
fof(x) = x
So, fof(x) = x.
d. gog (g circle g):
To find gog(x), we need to substitute g(x) into g(x). So we replace x in g(x) with g(x):
gog(x) = g(g(x))
Since g(x) = 3x - 5, we substitute it into g(x):
gog(x) = g(3x - 5)
Now, we substitute g(x) = 3x - 5 into the above expression:
gog(x) = 3(3x - 5) - 5
Simplifying the expression gives:
gog(x) = 9x - 15 - 5
Combining like terms gives:
gog(x) = 9x - 20
So, gog(x) = 9x - 20.
To summarize:
a. fog(x) = 9 - 3x
b. gof(x) = 7 - 3x
c. fof(x) = x
d. gog(x) = 9x - 20