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{:[f(x)=3x+2],[m(x)=(3)/(x)],[h(x)=3x^(2)-5x+4],[f(m(h(1)))=?]:}

f(x)=3x+2m(x)=3xh(x)=3x2−5x+4f(m(h(1)))=? \begin{array}{l}f(x)=3 x+2 \\ m(x)=\frac{3}{x} \\ h(x)=3 x^{2}-5 x+4 \\ f(m(h(1)))=?\end{array}

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Full solution

Q. f(x)=3x+2m(x)=3xh(x)=3x2−5x+4f(m(h(1)))=? \begin{array}{l}f(x)=3 x+2 \\ m(x)=\frac{3}{x} \\ h(x)=3 x^{2}-5 x+4 \\ f(m(h(1)))=?\end{array}
  1. Find h(1)h(1): First, we need to find the value of h(1)h(1) by substituting x=1x = 1 into the function h(x)h(x).
    h(x)=3x2−5x+4h(x) = 3x^2 - 5x + 4
    h(1)=3(1)2−5(1)+4h(1) = 3(1)^2 - 5(1) + 4
    h(1)=3−5+4h(1) = 3 - 5 + 4
    h(1)=2h(1) = 2
  2. Find m(h(1))m(h(1)): Next, we need to find the value of m(h(1))m(h(1)) by substituting h(1)h(1) into the function m(x)m(x).
    m(x)=3xm(x) = \frac{3}{x}
    m(h(1))=m(2)=32m(h(1)) = m(2) = \frac{3}{2}
  3. Find f(m(h(1)))f(m(h(1))): Finally, we need to find the value of f(m(h(1)))f(m(h(1))) by substituting m(h(1))m(h(1)) into the function f(x)f(x).\newlinef(x)=3x+2f(x) = 3x + 2\newlinef(m(h(1)))=f(32)=3∗(32)+2f(m(h(1))) = f(\frac{3}{2}) = 3*(\frac{3}{2}) + 2\newlinef(m(h(1)))=92+2f(m(h(1))) = \frac{9}{2} + 2\newlinef(m(h(1)))=92+42f(m(h(1))) = \frac{9}{2} + \frac{4}{2}\newlinef(m(h(1)))=132f(m(h(1))) = \frac{13}{2}

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