What is the smallest integer value of c such that the function f(x) = (x^2 + 1)/(x^2 - 4x + c) has a domain of all real numbers?
+208 the only way the expression \(\frac{x^2\:+\:1}{x^2\:-\:4x\:+\:c}\) is not real is if the denominator equals zero
\(x^2\:-\:4x\:+\:c=0 \)
discriminant is:
\((-4)^2-4c \\=16-4c\)
to have no real solutions:
\(16-4c<0 \\4c>16 \\c>4\)
smallest integer value is c=5
JP
+208 the only way the expression \(\frac{x^2\:+\:1}{x^2\:-\:4x\:+\:c}\) is not real is if the denominator equals zero
\(x^2\:-\:4x\:+\:c=0 \)
discriminant is:
\((-4)^2-4c \\=16-4c\)
to have no real solutions:
\(16-4c<0 \\4c>16 \\c>4\)
smallest integer value is c=5
JP
