Functions & Function Notation

Question

Let the function f be defined by y = f(x),where x and f(x) are real numbers. Find f(3),f(−4),f(k), and f(k² − 1).

f(x) = −x² − 3x + 1

f(3)=

f(−4)=

f(k)=

f(k² − 1)=

 

Answer 1

f(3) = -(3)^2 - 3(3) + 1

= -9 - 9 + 1

= -17

f(-4) = -(-4)^2 - 3(-4) + 1

= -16 + 12 + 1

= -3

f(k) = -k^2 -3k+1

f(k^2-1) = -(k^2-1)^2 - 3(k^2-1) + 1

= -(k^4 - 2k^2 + 1) - 3(k^2-1) + 1

= -k^4 + 2k^2 - 1 - 3k^2 + 3 + 1

= -k^4 - k^2 + 3