Question

Let f and g be real functions defined by f( x ) = 2x +1 And g( x) = 4x -7 .i) for what real numbers x, f(x) = g(x) ? and f( x) < g(x) ?

Answer 1

f(x)=2x+1 and g(x)=4x-7 are R to R, then find x such that f(x)=g(x), f(x)<g(x)

f(x)=g(x)

⇒ 2x+1=4x-7

⇒ -2x=-8

∴ x=4 satisfies f(x)=g(x)

f(x)<g(x)

⇒ f(x)-g(x)<0

⇒ 2x+1-(4x-7)<0

⇒ 2x+1-4x+7<0

⇒ -2x+8<0

⇒ 2x>8

∴ x>4 satisfies f(x)<g(x)