1. if f(x)=3^x-3^-x, find :f(2),f(-1)
2. if y1=x^2+3x-1 and y2=x-5,
find: a. y1+y2
b. y1-y2
c. y1(y2)
please show solution thanks.
f(2)=80/9
f(-1)=-8/3
Sure! Let's solve these step by step:
1. To find f(2) and f(-1) for the function f(x) = 3^x - 3^(-x), we need to substitute the values of 2 and -1 respectively into the equation.
a. f(2):
Substitute x = 2 into the equation:
f(2) = 3^2 - 3^(-2)
= 9 - 1/9
= 81/9 - 1/9
= 80/9
Therefore, f(2) = 80/9.
b. f(-1):
Substitute x = -1 into the equation:
f(-1) = 3^-1 - 3^(-(-1))
= 1/3 - 1/(1/3)
= 1/3 - 3
= 1/3 - 9/3
= -8/3
Therefore, f(-1) = -8/3.
2. Now let's solve the second part of the question. We have two equations:
y1 = x^2 + 3x - 1
y2 = x - 5
a. y1 + y2:
To find y1 + y2, we simply add the two equations together:
y1 + y2 = (x^2 + 3x - 1) + (x - 5)
= x^2 + 3x - 1 + x - 5
= x^2 + 4x - 6
Therefore, y1 + y2 = x^2 + 4x - 6.
b. y1 - y2:
To find y1 - y2, we subtract the second equation from the first equation:
y1 - y2 = (x^2 + 3x - 1) - (x - 5)
= x^2 + 3x - 1 - x + 5
= x^2 + 2x + 4
Therefore, y1 - y2 = x^2 + 2x + 4.
c. y1(y2):
To find y1(y2), we multiply the two equations together:
y1(y2) = (x^2 + 3x - 1)(x - 5)
= x^3 - 5x^2 + 3x^2 - 15x - x + 5
= x^3 - 2x^2 - 16x + 5
Therefore, y1(y2) = x^3 - 2x^2 - 16x + 5.
I hope this helps! Let me know if you have any other questions.